subject:(Nonsmooth analysis)

University of Ballarat

1. Ganjehlou, Asef Nazari. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.

Degree: PhD, 2009, University of Ballarat

URL: http://researchonline.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/39640 ; http://innopac.ballarat.edu.au/record=b1497526

This thesis is devoted to the development of algorithms for solving nonsmooth nonconvex problems. Some of these algorithms are derivative free methods.

Doctor of Philosophy

Subjects/Keywords: Mathematical optimization; Cluster analysis; Nonsmooth optimization; Australian Digital Thesis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ganjehlou, A. N. (2009). Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. (Doctoral Dissertation). University of Ballarat. Retrieved from http://researchonline.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/39640 ; http://innopac.ballarat.edu.au/record=b1497526

Chicago Manual of Style (16^th Edition):

Ganjehlou, Asef Nazari. “Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.” 2009. Doctoral Dissertation, University of Ballarat. Accessed March 06, 2021. http://researchonline.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/39640 ; http://innopac.ballarat.edu.au/record=b1497526.

MLA Handbook (7^th Edition):

Ganjehlou, Asef Nazari. “Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.” 2009. Web. 06 Mar 2021.

Vancouver:

Ganjehlou AN. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. [Internet] [Doctoral dissertation]. University of Ballarat; 2009. [cited 2021 Mar 06]. Available from: http://researchonline.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/39640 ; http://innopac.ballarat.edu.au/record=b1497526.

Council of Science Editors:

Ganjehlou AN. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. [Doctoral Dissertation]. University of Ballarat; 2009. Available from: http://researchonline.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/39640 ; http://innopac.ballarat.edu.au/record=b1497526

Freie Universität Berlin

2. Sack, Uli. Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen.

Degree: 2014, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-7442

► Mit dem EU weiten Verbot von bleihaltigen Loten in elektronischen Bauteilen ergibt sich die Notwendigkeit, Ersatzlegierungen mit vergleichbaren Verarbeitungseigenschaften und vergleichbarer Lebensdauer zu entwickeln. Numerische… (more)

▼ Mit dem EU weiten Verbot von bleihaltigen Loten in elektronischen Bauteilen ergibt sich die Notwendigkeit, Ersatzlegierungen mit vergleichbaren Verarbeitungseigenschaften und vergleichbarer Lebensdauer zu entwickeln. Numerische Simulationen der Evolution der Mikrostruktur können dazu beitragen, geeignete Kandidaten auszuwählen und damit den großen experimentellen Aufwand zu verringern bzw. zu fokussieren. Ziel dieser Arbeit ist zum einen ein numerisches Framework zur effizienten und robusten Simulation der Mikrostrukturevolution in binären Legierungen mit reellen Materialparametern zu erarbeiten. Dieses soll adaptive Finite-Elemente-Verfahren mit den schnellen Lösern für die Cahn-Hilliard-Gleichung und die elastischen Teilprobleme kombinieren. Zum anderen sollen die Nichtglatten Schur-Newton Verfahren zur Lösung der diskreten skalaren Cahn-Hilliard Gleichung auf den mehrkomponentigen Fall, d.h. mit vektorwertigem Ordnungsparameter, erweitert werden. Nach einführenden Bemerkungen zu Phasendiagrammen, Phasenseparation und Phasenfeldmodellen in Kapitel 1 wird in Kapitel 2 zunächst die anisotrope Allen-Cahn-Gleichung untersucht. Allen-Cahn-artige Probleme treten als Teilprobleme bei der Lösung der Cahn-Hilliard Gleichung in den Kapiteln 3 und 4 auf. Hier werden Existenz- und Eindeutigkeit von Lösungen mithilfe der Theorie maximal monotoner Operatoren bewiesen. Für die numerische Lösung werden ein adaptiver Ortsgitter-Verfeinerungszyklus für zeitabhängige Probleme und mehrere Varianten impliziter Euler-Zeitdiskretisierung eingeführt. Für letztere wird Stabilität bewiesen und numerische Experimente illustrieren die Genauigkeit der Diskretisierungen sowie den Verlust der Rotationsinvarianz unter Anisotropie. Kapitel 3 fügt bereits existierende und neu entwickelte numerische Werkzeuge zu einem Simulationstool für Mikrostrukturevolutionen in binären Legierungen zusammen. Wesentliche Bausteine sind dabei der adaptive Gitterverfeinerungszyklus aus Kapitel 2, der NSNMG Löser, ein Quantifizierungsalgorithmus für den Grad der Vergröberung der Mikrostruktur und ein Quotientenraum-Mehrgitterverfahren für die indefiniten Elastizitätsprobleme. Die Anwendung dieses Simulationstools für eine eutektische AgCu-Legierung zeigt nur marginalen Einfluss der Elastizität auf die Vergröberung im betrachteten Setting. Die Verwendung eines glatten Potentials anstelle des logarithmischen verfälscht die Vergröberungsdynamik hingegen erheblich. Im letzten Kapitel wird für die vektorwertige Cahn- Hilliard-Gleichung eine vereinheitlichende Formulierung für die diskretisierten Ortsprobleme hergeleitet, welche die direkte Anwendung des NSNMG Verfahrens erlaubt. Existenz und Eindeutigkeit von diskreten Lösungen werden gezeigt und numerische Beispiele illustrieren die Robustheit des Verfahrens bzgl. Temperatur und Anzahl der Komponenten. Advisors/Committee Members: [email protected] (contact), m (gender), Prof. Dr. Ralf Kornhuber (firstReferee), Prof. Dr. Harald Garcke (furtherReferee).

Subjects/Keywords: phase separation; phasefield models; Cahn-Hilliard; nonsmooth Newton methods; multigrid; finite elements; 500 Naturwissenschaften und Mathematik::510 Mathematik::518 Numerische Analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Sack, U. (2014). Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-7442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sack, Uli. “Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen.” 2014. Thesis, Freie Universität Berlin. Accessed March 06, 2021. http://dx.doi.org/10.17169/refubium-7442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sack, Uli. “Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen.” 2014. Web. 06 Mar 2021.

Vancouver:

Sack U. Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen. [Internet] [Thesis]. Freie Universität Berlin; 2014. [cited 2021 Mar 06]. Available from: http://dx.doi.org/10.17169/refubium-7442.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sack U. Numerische Simulation von Phasentrennung in zwei- und mehrkomponentigen Systemen. [Thesis]. Freie Universität Berlin; 2014. Available from: http://dx.doi.org/10.17169/refubium-7442

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Ballarat

3. Ganjehlou, Asef Nazari. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.

Degree: PhD, 2009, University of Ballarat

URL: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243 ; http://library.federation.edu.au/record=b1497526

This thesis is devoted to the development of algorithms for solving nonsmooth nonconvex problems. Some of these algorithms are derivative free methods.

Doctor of Philosophy

Subjects/Keywords: Mathematical optimization; Cluster analysis; Nonsmooth optimization; Australian Digital Thesis

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ganjehlou, A. N. (2009). Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. (Doctoral Dissertation). University of Ballarat. Retrieved from http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243 ; http://library.federation.edu.au/record=b1497526

Chicago Manual of Style (16^th Edition):

Ganjehlou, Asef Nazari. “Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.” 2009. Doctoral Dissertation, University of Ballarat. Accessed March 06, 2021. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243 ; http://library.federation.edu.au/record=b1497526.

MLA Handbook (7^th Edition):

Ganjehlou, Asef Nazari. “Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis.” 2009. Web. 06 Mar 2021.

Vancouver:

Ganjehlou AN. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. [Internet] [Doctoral dissertation]. University of Ballarat; 2009. [cited 2021 Mar 06]. Available from: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243 ; http://library.federation.edu.au/record=b1497526.

Council of Science Editors:

Ganjehlou AN. Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis. [Doctoral Dissertation]. University of Ballarat; 2009. Available from: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243 ; http://library.federation.edu.au/record=b1497526

Louisiana State University

4. Zabic, Stanislav. Impulsive systems.

Degree: PhD, Applied Mathematics, 2005, Louisiana State University

URL: etd-07122005-145903 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2157

► Impulsive systems arise when dynamics produce discontinuous trajectories. Discontinuties occur when movements of states happen over a small interval that resembles a point-mass measure. We… (more)

▼ Impulsive systems arise when dynamics produce discontinuous trajectories. Discontinuties occur when movements of states happen over a small interval that resembles a point-mass measure. We adopt the formalism in which the controlled dynamic inclusion is the sum of a slow and a fast time velocities belonging to two distinct vector fields. Fast time velocities are controlled by a vector valued Borel measure. The trajectory of impulsive systems is a function of bounded variation. To give a definition of solutions, a notion of graph completion of the control measure is needed. In the nonimpulsive case, a solution can be defined as a limit of a sequence of approximate arcs which converge to an absolutely continuous arc. Even in simple cases it shows that this is not a good way to define solutions of the impulsive systems. The key point is that the approximate controls converge to two different graph completions. Introduction contains examples in which we discuss the need for the impulsive systems, their relation to the hybrid systems. A paradox related to the convergence of approximate arcs is illustrated. Chapter 1 contains preliminary results in nonimpulsive systems and mathematical analysis in general. Chapter 2 precisely defines impulsive systems, discusses two different solution concepts and proves properties of graph completions. Chapter 3 is entirely dedicated to adaptation of the Euler approximating schemes to the impulsive system. Two different schemes are offered. For one of them a measure which drives the system needs to be specified. We used it to show that the approximate trajectories graph-converge to a solution. The other sampling technique constructs a measure along with the solution. We use it in Chapter 4. Chapter 4 deals with issues when a trajectory remains within a closed set. This property is called invariance. Notions of weak and strong invariance for the impulsive systems are introduced and proximal characterizations are proved. In the case of weak invariance, two proofs are offered: one based on a sampling technique from Chapter 3 and other based on selections theory. The final chapter of this thesis discusses directions in future research.

Subjects/Keywords: nonsmooth analysis; hybrid systems; impulsive systems; control theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zabic, S. (2005). Impulsive systems. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-07122005-145903 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2157

Chicago Manual of Style (16^th Edition):

Zabic, Stanislav. “Impulsive systems.” 2005. Doctoral Dissertation, Louisiana State University. Accessed March 06, 2021. etd-07122005-145903 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2157.

MLA Handbook (7^th Edition):

Zabic, Stanislav. “Impulsive systems.” 2005. Web. 06 Mar 2021.

Vancouver:

Zabic S. Impulsive systems. [Internet] [Doctoral dissertation]. Louisiana State University; 2005. [cited 2021 Mar 06]. Available from: etd-07122005-145903 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2157.

Council of Science Editors:

Zabic S. Impulsive systems. [Doctoral Dissertation]. Louisiana State University; 2005. Available from: etd-07122005-145903 ; https://digitalcommons.lsu.edu/gradschool_dissertations/2157

Northeastern University

5. Rodriguez Vaqueiro, Yolanda. Compressive sensing for electromagnetic imaging using a nesterov-based algorithm.

Degree: PhD, Department of Electrical and Computer Engineering, 2015, Northeastern University

URL: http://hdl.handle.net/2047/D20194129

► Compressive Sensing (CS) is a relatively novel signal processing theory; it states that sparse signals can be recovered using far fewer samples or measurements than… (more)

Subjects/Keywords: backpropagation; compressive sensing; Fourier; imaging; Signal processing; Mathematical models; Imaging systems in medicine; Mathematical models; Nonsmooth optimization; Convex programming; Radar; Electromagnetic waves; Back propagation (Artificial intelligence); Fourier analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rodriguez Vaqueiro, Y. (2015). Compressive sensing for electromagnetic imaging using a nesterov-based algorithm. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20194129

Chicago Manual of Style (16^th Edition):

Rodriguez Vaqueiro, Yolanda. “Compressive sensing for electromagnetic imaging using a nesterov-based algorithm.” 2015. Doctoral Dissertation, Northeastern University. Accessed March 06, 2021. http://hdl.handle.net/2047/D20194129.

MLA Handbook (7^th Edition):

Rodriguez Vaqueiro, Yolanda. “Compressive sensing for electromagnetic imaging using a nesterov-based algorithm.” 2015. Web. 06 Mar 2021.

Vancouver:

Rodriguez Vaqueiro Y. Compressive sensing for electromagnetic imaging using a nesterov-based algorithm. [Internet] [Doctoral dissertation]. Northeastern University; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/2047/D20194129.

Council of Science Editors:

Rodriguez Vaqueiro Y. Compressive sensing for electromagnetic imaging using a nesterov-based algorithm. [Doctoral Dissertation]. Northeastern University; 2015. Available from: http://hdl.handle.net/2047/D20194129

6. Le Thi, Huong. Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition.

Degree: Docteur es, Mathématiques, 2017, Université Côte d'Azur (ComUE)

URL: http://www.theses.fr/2017AZUR4033

►

La motivation industrielle et mécanique du problème sera présentée pour un problème continu: élasticité linéaire avec une contrainte unilatérale. Un système masse-ressort avec un contact… (more)

▼

La motivation industrielle et mécanique du problème sera présentée pour un problème continu: élasticité linéaire avec une contrainte unilatérale. Un système masse-ressort avec un contact unilatéral en découle par discrétisation. Le but de cette thèse est d'étudier ces systèmes à vibro-impact de N degrés de liberté avec un contact unilatéral. Le système résultant est linéaire en l'absence de contact; Il est régi par une loi d'impact autrement. L'auteur identifie les modes non linéaires qui présentent une phase de contact collant pour un modèle à deux degrés de liberté en présence d'un obstacle rigide. L'application de premier retour de Poincaré est un outil fondamental pour étudier la dynamique près de solutions périodiques. Étant donné que la section de Poincaré est un sous-ensemble de l'interface de contact dans l'espace des phases, elle peut être tangente aux orbites pour les contacts rasants et conduire à une singularité en « racine carrée » déjà connue en Mécanique. Cette singularité est revisitée dans un cadre mathématique rigoureux. Elle implique la discontinuité du temps de premier retour. Enfin, l’instabilité des modes linéaire rasants est abordée.

The mechanical motivation is presented for a PDE with a constraint. The purpose of this thesis is to study N degree-of-freedom vibro-impact systems with an unilateral contact. The resulting system is linear in the absence of contact; it is governed by an impact law otherwise. The author identifies some nonlinear modes that display a sticking phase. The First Return Map is a fundamental tool to explore periodic solutions. Since the Poincaré section is a subset of the contact interface in the phase-space, it can be tangent to orbits which yields the well-known square-root singularity. This singularity is here revisited in a rigorous mathematical framework. Moreover, the study of this singularity implies a more important singularity: the discontinuity of the first return time. Finally, the square-root dynamics near the linear grazing modes which may lead to the instability of these linear grazing modes is studied.

Advisors/Committee Members: Junca, Stéphane (thesis director).

Subjects/Keywords: Analyse non lisse; Systèmes discrets à vibro-impact; Contact unilatéral; Solutions périodiques; Application de Poincaré; Nonsmooth analysis; Vibro-impact systems; Unilateral contact; Periodic solutions; Poincaré map

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Le Thi, H. (2017). Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition. (Doctoral Dissertation). Université Côte d'Azur (ComUE). Retrieved from http://www.theses.fr/2017AZUR4033

Chicago Manual of Style (16^th Edition):

Le Thi, Huong. “Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition.” 2017. Doctoral Dissertation, Université Côte d'Azur (ComUE). Accessed March 06, 2021. http://www.theses.fr/2017AZUR4033.

MLA Handbook (7^th Edition):

Le Thi, Huong. “Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition.” 2017. Web. 06 Mar 2021.

Vancouver:

Le Thi H. Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition. [Internet] [Doctoral dissertation]. Université Côte d'Azur (ComUE); 2017. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2017AZUR4033.

Council of Science Editors:

Le Thi H. Sur des solutions périodiques de systèmes discrets à vibro-impact avec un contact unilatéral : On some periodic solutions of discrete vibro-impact systems with a unilateral contact condition. [Doctoral Dissertation]. Université Côte d'Azur (ComUE); 2017. Available from: http://www.theses.fr/2017AZUR4033

7. WAN JIE. Stable Segment Formation Control of Multi-Robot System.

Degree: 2011, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/31618

Subjects/Keywords: formation control; artificial potential; multi-robot system; nonsmooth analysis; stability

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

JIE, W. (2011). Stable Segment Formation Control of Multi-Robot System. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/31618

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

JIE, WAN. “Stable Segment Formation Control of Multi-Robot System.” 2011. Thesis, National University of Singapore. Accessed March 06, 2021. http://scholarbank.nus.edu.sg/handle/10635/31618.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

JIE, WAN. “Stable Segment Formation Control of Multi-Robot System.” 2011. Web. 06 Mar 2021.

Vancouver:

JIE W. Stable Segment Formation Control of Multi-Robot System. [Internet] [Thesis]. National University of Singapore; 2011. [cited 2021 Mar 06]. Available from: http://scholarbank.nus.edu.sg/handle/10635/31618.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

JIE W. Stable Segment Formation Control of Multi-Robot System. [Thesis]. National University of Singapore; 2011. Available from: http://scholarbank.nus.edu.sg/handle/10635/31618

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Louisiana State University

8. Barnard, Richard Charles. Hamilton-Jacobi theory for optimal control problems on stratified domains.

Degree: PhD, Applied Mathematics, 2010, Louisiana State University

URL: etd-10022010-115320 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3288

► This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz… (more)

Subjects/Keywords: nonsmooth analysis; stratified domains; Hamilton-Jacobi; proximal normal; invariance; Mayer problem; value function

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APA (6^th Edition):

Barnard, R. C. (2010). Hamilton-Jacobi theory for optimal control problems on stratified domains. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-10022010-115320 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3288

Chicago Manual of Style (16^th Edition):

Barnard, Richard Charles. “Hamilton-Jacobi theory for optimal control problems on stratified domains.” 2010. Doctoral Dissertation, Louisiana State University. Accessed March 06, 2021. etd-10022010-115320 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3288.

MLA Handbook (7^th Edition):

Barnard, Richard Charles. “Hamilton-Jacobi theory for optimal control problems on stratified domains.” 2010. Web. 06 Mar 2021.

Vancouver:

Barnard RC. Hamilton-Jacobi theory for optimal control problems on stratified domains. [Internet] [Doctoral dissertation]. Louisiana State University; 2010. [cited 2021 Mar 06]. Available from: etd-10022010-115320 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3288.

Council of Science Editors:

Barnard RC. Hamilton-Jacobi theory for optimal control problems on stratified domains. [Doctoral Dissertation]. Louisiana State University; 2010. Available from: etd-10022010-115320 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3288

9. Zhang, Jin. Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems.

Degree: Department of Mathematics and Statistics, 2014, University of Victoria

URL: http://hdl.handle.net/1828/5762

► The main purpose of this dissertation is to investigate necessary optimality conditions for a class of very general nonsmooth optimization problems called the mathematical program… (more)

▼ The main purpose of this dissertation is to investigate necessary optimality conditions for a class of very general nonsmooth optimization problems called the mathematical program with geometric constraints (MPGC). The geometric constraint means that the image of certain mapping is included in a nonempty and closed set. We first study the conventional nonlinear program with equality, inequality and abstract set constraints as a special case of MPGC. We derive the enhanced Fritz John condition and from which, we obtain the enhanced Karush-Kuhn-Tucker (KKT) condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity implies the existence of a local error bound. We also give a tighter upper estimate for the Fréchet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. We then consider a more general MPGC where the image of the mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. One of the technical difficulties in obtaining such a result in an infinite dimensional space is that no compactness result can be used to show the existence of local minimizers of a perturbed problem. We employ the celebrated Ekeland's variational principle to obtain the results instead. We then apply our results to the study of exact penalty and sensitivity analysis. We also study a special class of MPCG named mathematical programs with equilibrium constraints (MPECs). We argue that the MPEC-linear independence constraint qualification is not a constraint qualification for the strong (S-) stationary condition when the objective function is nonsmooth. We derive the enhanced Fritz John Mordukhovich (M-) stationary condition for MPECs. From this enhanced Fritz John M-stationary condition we introduce the associated MPEC generalized pseudonormality and quasinormality condition and build the relations between them and some other widely used MPEC constraint qualifications. We give upper estimates for the subdifferential of the value function in terms of the enhanced M- and C-multipliers respectively. Besides, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian-Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the existence of local error bounds. We further extend the new result to the MPECs. Advisors/Committee Members: Ye, Juan Juan (supervisor).

Subjects/Keywords: Constraint Qualifications; Exact penalty; mathematical programs with equilibrium constraints; Nonsmooth Analysis; Optimality Conditions; Sensitivity analysis

…analysis This section contains some background material on nonsmooth analysis and preliminary… …nonsmooth optimization problems and their applications. Only ﬁrst-order necessary conditions are… …nonsmooth mathematical programming problems. 1.1 Background on enhanced optimality conditions… …a largely overlooked analysis by Hestenes [30] for the case of smooth… …enhanced Fritz John condition for nonsmooth problems with 5 no abstract set constraint can be…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhang, J. (2014). Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems. (Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/5762

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhang, Jin. “Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems.” 2014. Thesis, University of Victoria. Accessed March 06, 2021. http://hdl.handle.net/1828/5762.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhang, Jin. “Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems.” 2014. Web. 06 Mar 2021.

Vancouver:

Zhang J. Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems. [Internet] [Thesis]. University of Victoria; 2014. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1828/5762.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhang J. Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems. [Thesis]. University of Victoria; 2014. Available from: http://hdl.handle.net/1828/5762

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

10. Khalil, Nathalie. Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications.

Degree: Docteur es, Mathématiques, 2017, Brest

URL: http://www.theses.fr/2017BRES0095

► Le projet de cette thèse est double. Le premier concerne l’extension des résultats précédents sur les conditions nécessaires d’optimalité pour des problèmes avec contraintes d’état,… (more)

▼ Le projet de cette thèse est double. Le premier concerne l’extension des résultats précédents sur les conditions nécessaires d’optimalité pour des problèmes avec contraintes d’état, dans le cadre du contrôle optimal ainsi que dans le cadre de calcul des variations. Le deuxième objectif consiste à travailler sur deux nouveaux aspects de recherche : dériver des résultats de viabilité pour une classe de systèmes de contrôle avec des contraintes d’état dans lesquels les conditions dites ‘standard inward pointing conditions’ sont violées; et établir les conditions nécessaires d’optimalité pour des problèmes de minimisation de coût moyen éventuellement perturbés par des paramètres inconnus.Dans la première partie, nous examinons les conditions nécessaires d’optimalité qui jouent un rôle important dans la recherche de candidats pour être des solutions optimales parmi toutes les solutions admissibles. Cependant, dans les problèmes d’optimisation dynamique avec contraintes d’état, certaines situations pathologiques pourraient survenir. Par exemple, il se peut que le multiplicateur associé à la fonction objective (à minimiser) disparaisse. Dans ce cas, la fonction objective à minimiser n’intervient pas dans les conditions nécessaires de premier ordre: il s’agit du cas dit anormal. Un phénomène pire, appelé le cas dégénéré montre que, dans certaines circonstances, l’ensemble des trajectoires admissibles coïncide avec l’ensemble des candidats minimiseurs. Par conséquent, les conditions nécessaires ne donnent aucune information sur les minimiseurs possibles.Pour surmonter ces difficultés, de nouvelles hypothèses supplémentaires doivent être imposées, appelées les qualifications de la contrainte. Nous étudions ces deux problèmes (normalité et non dégénérescence) pour des problèmes de contrôle optimal impliquant des contraintes dynamiques exprimées en termes d’inclusion différentielle, lorsque le minimiseur a son point de départ dans une région où la contrainte d’état est non lisse. Nous prouvons que sous une information supplémentaire impliquant principalement le cône tangent de Clarke, les conditions nécessaires sous la forme dite ‘Extended Euler-Lagrange condition’ sont satisfaites en forme normale et non dégénérée pour deux classes de problèmes de contrôle optimal avec contrainte d’état. Le résultat sur la normalité est également appliqué pour le problème de calcul des variations avec contrainte d’état.Dans la deuxième partie de la thèse, nous considérons d’abord une classe de systèmes de contrôle avec contrainte d’état pour lesquels les qualifications de la contrainte standard du ‘premier ordre’ ne sont pas satisfaites, mais une qualification de la contrainte d’ordre supérieure (ordre 2) est satisfaite.Nous proposons une nouvelle construction des trajectoires admissibles (dit un résultat de viabilité) et nous étudions des exemples (tels que l’intégrateur non holonomique de Brockett) fournissant en plus un résultat d’estimation non linéaire. L’autre sujet de la deuxième partie de la thèse concerne l’étude d’une classe de… Advisors/Committee Members: Bettiol, Piernicola (thesis director).

Subjects/Keywords: Contrôle optimal; Théorie de contrôle; Conditions nécessaires d’optimalité; Normalité; Non-dégénérescence; Analyse non lisse; Calcul des variations; Optimal control; Control theory; Necessary optimality conditions; Normality; Non-degeneracy; Nonsmooth Analysis; Calculus of variations; 515.4642

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APA (6^th Edition):

Khalil, N. (2017). Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications. (Doctoral Dissertation). Brest. Retrieved from http://www.theses.fr/2017BRES0095

Chicago Manual of Style (16^th Edition):

Khalil, Nathalie. “Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications.” 2017. Doctoral Dissertation, Brest. Accessed March 06, 2021. http://www.theses.fr/2017BRES0095.

MLA Handbook (7^th Edition):

Khalil, Nathalie. “Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications.” 2017. Web. 06 Mar 2021.

Vancouver:

Khalil N. Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications. [Internet] [Doctoral dissertation]. Brest; 2017. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2017BRES0095.

Council of Science Editors:

Khalil N. Conditions d'optimalité pour des problèmes en contrôle optimal et applications : Optimality conditions for optimal control problems and applications. [Doctoral Dissertation]. Brest; 2017. Available from: http://www.theses.fr/2017BRES0095

11. Glotfelter, Paul. Specification composition and controller synthesis for robotic systems.

Degree: PhD, Electrical and Computer Engineering, 2019, Georgia Tech

URL: http://hdl.handle.net/1853/61238

► From precision agriculture to autonomous-transportation systems, robotic systems have been proposed to accomplish a number of tasks. However, these systems typically require satisfaction of multiple… (more)

Subjects/Keywords: Boolean composition; Nonsmooth analysis; Differential inclusions; Multi-robot systems; Robotic systems; Collision avoidance; Leader follower

…136 Appendix C: Nonsmooth Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 138 C… …Boolean expression; as such, this thesis utilizes nonsmooth analysis, as in [14, 15, 16… …nonsmooth analysis in the context of this thesis: the generalized gradient and its associated… …Set-Valued Analysis . . . . . . . . . . . . . . . . . . . . . . . 134 B.4 Related Work… …extends the theory on barrier functions to nonsmooth barrier functions and, subsequently, to…

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APA (6^th Edition):

Glotfelter, P. (2019). Specification composition and controller synthesis for robotic systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/61238

Chicago Manual of Style (16^th Edition):

Glotfelter, Paul. “Specification composition and controller synthesis for robotic systems.” 2019. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/61238.

MLA Handbook (7^th Edition):

Glotfelter, Paul. “Specification composition and controller synthesis for robotic systems.” 2019. Web. 06 Mar 2021.

Vancouver:

Glotfelter P. Specification composition and controller synthesis for robotic systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2019. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/61238.

Council of Science Editors:

Glotfelter P. Specification composition and controller synthesis for robotic systems. [Doctoral Dissertation]. Georgia Tech; 2019. Available from: http://hdl.handle.net/1853/61238

12. Sadikhov, Teymur. Stability, dissipativity, and optimal control of discontinuous dynamical systems.

Degree: Aerospace Engineering, 2015, Georgia Tech

URL: http://hdl.handle.net/1853/53635

► Discontinuous dynamical systems and multiagent systems are encountered in numerous engineering applications. This dissertation develops stability and dissipativity of nonlinear dynamical systems with discontinuous right-hand… (more)

▼ Discontinuous dynamical systems and multiagent systems are encountered in numerous engineering applications. This dissertation develops stability and dissipativity of nonlinear dynamical systems with discontinuous right-hand sides, optimality of discontinuous feed-back controllers for Filippov dynamical systems, almost consensus protocols for multiagent systems with innaccurate sensor measurements, and adaptive estimation algorithms using multiagent network identifiers. In particular, we present stability results for discontinuous dynamical systems using nonsmooth Lyapunov theory. Then, we develop a constructive feedback control law for discontinuous dynamical systems based on the existence of a nonsmooth control Lyapunov function de fined in the sense of generalized Clarke gradients and set-valued Lie derivatives. Furthermore, we develop dissipativity notions and extended Kalman-Yakubovich-Popov conditions and apply these results to develop feedback interconnection stability results for discontinuous systems. In addition, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Then, we provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Furthermore, we address the consensus problem for a group of agent robots with uncertain interagent measurement data, and show that the agents reach an almost consensus state and converge to a set centered at the centroid of agents initial locations. Finally, we develop an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies that identifies the system state and plant parameters online. Advisors/Committee Members: Haddad, Wassim (advisor), Feron, Eric (committee member), Egerstedt, Magnus (committee member), Prasad, J. V. R. (committee member), Holzinger, Marcus (committee member).

Subjects/Keywords: Multiagent systems; Optimality; Dissipativity; Universal controller; Adaptive estimation; Sensor uncertainty; Set-valued analysis; Set-valued maps; Nonsmooth systems

…139 Vita 145 viii List of Figures 3.1 Phase portrait of the open-loop nonsmooth… …harmonic oscillator. . . . 29 3.2 Phase portrait of the closed-loop nonsmooth harmonic… …dynamical systems using nonsmooth Lyapunov theory. Then, we develop a constructive feedback… …control law for discontinuous dynamical systems based on the existence of a nonsmooth control… …online. The consideration of nonsmooth Lyapunov functions for proving stability of feedback…

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APA (6^th Edition):

Sadikhov, T. (2015). Stability, dissipativity, and optimal control of discontinuous dynamical systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/53635

Chicago Manual of Style (16^th Edition):

Sadikhov, Teymur. “Stability, dissipativity, and optimal control of discontinuous dynamical systems.” 2015. Doctoral Dissertation, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/53635.

MLA Handbook (7^th Edition):

Sadikhov, Teymur. “Stability, dissipativity, and optimal control of discontinuous dynamical systems.” 2015. Web. 06 Mar 2021.

Vancouver:

Sadikhov T. Stability, dissipativity, and optimal control of discontinuous dynamical systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/53635.

Council of Science Editors:

Sadikhov T. Stability, dissipativity, and optimal control of discontinuous dynamical systems. [Doctoral Dissertation]. Georgia Tech; 2015. Available from: http://hdl.handle.net/1853/53635

13. Dhar, Gaurav. Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data.

Degree: Docteur es, Mathematiques et applications, 2020, Limoges

URL: http://www.theses.fr/2020LIMO0050

► L’objectif de cette thèse est d’obtenir des conditions nécessaires d’optimalité du premier ordre sous la forme d’un principe du maximum de Pontryagin (en abrégé PMP)… (more)

▼ L’objectif de cette thèse est d’obtenir des conditions nécessaires d’optimalité du premier ordre sous la forme d’un principe du maximum de Pontryagin (en abrégé PMP) pour des problèmes de contrôle échantillonné optimal avec temps d’échantillonnage libres, contraintes d’état et coûts de Mayer non lisses. Le Chapitre 1 est consacré aux notations et espaces fonctionnels utiles pour décrire les problèmes de contrôle échantillonné optimal qui seront rencontrés dans le manuscrit. Dans le Chapitre 2, nous obtenons une condition nécessaire d’optimalité lorsque les temps d’échantillonnage peuvent être choisis librement qui est appelée condition de continuité de la fonction Hamiltonienne. Rappelons que la fonction Hamiltonienne qui décrit l’évolution du Hamiltonien avec les valeurs de la trajectoire optimale et du contrôle échantillonné optimal est, en général, discontinue quand les temps d’échantillonnage sont fixés. Notre résultat démontre que la continuité de la fonction Hamiltonienne est retrouvée pour les contrôles échantillonnés optimaux avec temps d’échantillonnage optimaux. Pour terminer, nous implémentons une méthode de tir basée sur la condition de continuité de la fonction Hamiltonienne pour déterminer numériquement les temps d’échantillonnage optimaux dans deux exemples linéaires-quadratiques. Dans le Chapitre 3, nous obtenons un PMP pour des problèmes de contrôle échantillonné optimal avec contraintes d’état. Nous obtenons que les vecteurs adjoints sont solutions de problèmes de Cauchy-Stieltjes définis par des mesures de Borel associées à des fonctions à variation bornée. De plus, nous trouvons que, sous quelques hypothèses assez générales, toute trajectoire admissible (associée à un contrôle échantillonné) rebondit nécessairement sur les contraintes d’état. Nous exploitons ce phénomène de trajectoires rebondissantes pour implémenter une méthode indirecte qu’on utilise pour résoudre numériquement quelques exemples simples de problèmes de contrôle échantillonné optimal avec contraintes d’état. Dans le Chapitre 4, nous obtenons un PMP pour des problèmes de contrôle échantillonné optimal avec coûts de Mayer non lisses. Notre preuve est uniquement basée sur les outils de l’analyse non lisse et n’utilise aucune technique de régularisation. Nous déterminons l’existence d’une sélection dans le sous-différentiel de la fonction de coût de Mayer non lisse en établissant un résultat plus général sur l’existence d’un vecteur séparant universel pour les ensembles convexes compacts. En appliquant ce résultat, appelé théorème de vecteur séparant universel, nous obtenons un PMP pour des problèmes de contrôle échantillonné optimal avec coûts de Mayer non lisses où la condition de transversalité sur le vecteur adjoint est donnée par une inclusion dans le sous-différentiel de la fonction de coût de Mayer non lisse. Pour obtenir les conditions d’optimalité sous la forme d’un PMP, nous utilisons différentes techniques de perturbation sur le contrôle optimal. Pour traiter les contraintes d’état, nous pénalisons la distance à ces… Advisors/Committee Members: Adly, Samir (thesis director), Bourdin, Loïc (thesis director).

Subjects/Keywords: Contrôle optimal; Contrôle échantillonné; Principe du maximum de Pontryagin; Principe variation-nel d’Ekeland; Temps d’échantillonnage optimaux; Continuité de la fonction Hamiltonienne; Contraintes d’état; Problèmes de Cauchy-Stieltjes; Analyse non lisse; Méthodes numériques indirectes; Méthodes de tir; Optimal control; Sampled-data control; Pontryagin maximum principle; Ekeland variational principle,; Optimal sampling times; Hamiltonian continuity; Running state constraints; Cauchy-Stieltjes problems; Nonsmooth analysis; Indirect numerical methods; Shooting methods; 519.6

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dhar, G. (2020). Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data. (Doctoral Dissertation). Limoges. Retrieved from http://www.theses.fr/2020LIMO0050

Chicago Manual of Style (16^th Edition):

Dhar, Gaurav. “Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data.” 2020. Doctoral Dissertation, Limoges. Accessed March 06, 2021. http://www.theses.fr/2020LIMO0050.

MLA Handbook (7^th Edition):

Dhar, Gaurav. “Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data.” 2020. Web. 06 Mar 2021.

Vancouver:

Dhar G. Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data. [Internet] [Doctoral dissertation]. Limoges; 2020. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2020LIMO0050.

Council of Science Editors:

Dhar G. Contributions en théorie du contrôle échantillonné optimal avec contraintes d’état et données non lisses : Contributions in optimal sampled-data control theory with state constraintsand nonsmooth data. [Doctoral Dissertation]. Limoges; 2020. Available from: http://www.theses.fr/2020LIMO0050

14. ΣΤΑΥΡΟΥΛΑΚΗΣ, ΓΕΩΡΓΙΟΣ. ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ.

Degree: 1991, Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); Aristotle University Of Thessaloniki (AUTH)

URL: http://hdl.handle.net/10442/hedi/1628

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THE STATIC ANALYSIS PROBLEM FOR STRUCTURES WITH INTERFACES IS STUDIED IN THE FRAMEWORK OF INEQUALITY (NONSMOOTH) MECHANICS. MONOTONE AND NONMONOTONE, POSSIBLYMULTIVALUED INTERFACE LAWS CAN BE… (more)

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THE STATIC ANALYSIS PROBLEM FOR STRUCTURES WITH INTERFACES IS STUDIED IN THE FRAMEWORK OF INEQUALITY (NONSMOOTH) MECHANICS. MONOTONE AND NONMONOTONE, POSSIBLYMULTIVALUED INTERFACE LAWS CAN BE PRODUCED FROM APPROPRIATELY DEFINED CONVEX AND NONCONVEX, GENERALLY NONDIFFERENTIABLE SUPERPOTENTIALS BY MEANS OF GENERALIZATIONS OF THE DIFFERENTIAL NOTION OF SMOOTH ANALYSIS: SUBDIFFERENTIAL OPERATOR IN THE SENSE OF J.J. MOREAU IS USED FOR MODELLING OF MONOTONE LAWS, GENERALIZEDSUBDIFFERENTIAL OPERATOR IN THE SENSE OF F.H. CLARKE AND THE QUASIDIFFERENTIALOPERATOR IN THE SENSE OF V.F. DEM'YANOV ARE USED FOR NONMONOTONE LAWS. THE STATIC STRUCTURAL ANALYSIS PROBLEM FOR STRUCTURES WITH INTERFACES IS WRITTEN IN THE GENERAL FORM OF A VARIATIONAL-HEMIVARIATIONAL INEQUALITY AND SYSTEM OF VARIATIONAL INEQUALITIES BASED ON THE ASSUMPTION FOR THE INTERFACE LAWS USED. EXISTENCE, APPROXIMATION RESULTS AND SOLVABILITY CONDITIONS FOR THE SOLUTION OF MODEL INEQUALITY PROBLEMS ARE DERIVED. MATHEMATICAL PROGRAMMING ALGORITHMS, APPROPRIATELY MODIFIED ARE USED FOR THE NUMERICAL SOLUTION OF THE PROBLEMS IN THE FRAMEWORK OF THE FINITE ELEMENT METHOD. IN PARTICULAR THE FOLLOWING TYPES OF PROBLEMSARE FORMULATED AND SOLVED: QUADRATIC PROGRAMMING PROBLEMS (USE OF ITERATIVE E.G. HILDRETH-D'ESOPO ALGORITHM), LINEAR (POSSIBLY NONSYMMETRIC) COMPLEMENTARITY PROBLEMS (CONTINUATION, SIMPLEX- TYPE METHOD OF LEMKE) AND PROBLEMS OF CONVEX AND NONCONVEX NONSMOOTH OPTIMIZATION (BUNDLE, NONSMOOTH OPTIM TYPE ALGORITHMS OFLEMARECHAL). ALGORITHMS FOR THE SOLUTION OF STRUCTURES WITH MONOTONE LAWS ARE COMBINED, IN THE FRAMEWORK OF A MULTILEVEL OPTIMIZATION (TWO PHASE) SCHEME, FORTHE SOLUTION OF STRUCTURES WITH NONMONOTONE LAWS, BASED ON THE SYSTEM OF VARIATIONAL INEQUALITIES FORMULATION OF THE PROBLEM. THE THEORY IS ILLUSTRATED BY MEANS OF NUMERICAL EXAMPLES CONCERNING: THE ANALYSIS OF SANDWICH AND LAYERED COMPOSITE STRUCTURES WITH DELAMINATION, THE STATIC ANALYSIS OF CRACKED AND MULTI-BODY STRUCTURES, THE ANALYSIS OF ELASTIC AND RIGID STAMP PROBLEMS AND THE ANALYSIS OF MATERIAL INCLUSION PROBLEMS IN COMPOSITES FOR VARIOUS INTERFACE LAWS.

ΠΡΟΒΛΗΜΑΤΑ ΣΤΑΤΙΚΟΥ ΥΠΟΛΟΓΙΣΜΟΥ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ ΜΟΡΦΩΝΟΝΤΑΙ ΚΑΙ ΜΕΛΕΤΩΝΤΑΙ ΣΤΑ ΠΛΑΙΣΙΑ ΤΗΣ ΑΝΙΣΟΤΙΚΗΣ (ΜΗ-ΛΕΙΑΣ) ΜΗΧΑΝΙΚΗΣ. ΜΟΝΟΤΟΝΟΙ ΚΑΙ ΜΗ-ΜΟΝΟΤΟΝΟΙ,ΠΙΘΑΝΩΣ ΠΟΛΥΣΗΜΑΝΤΟΙ ΝΟΜΟΙ ΔΙΕΠΙΦΑΝΕΙΑΣ ΠΑΡΑΓΟΝΤΑΙ ΑΠΟ ΚΑΤΑΛΛΗΛΑ ΟΡΙΣΜΕΝΑ ΚΥΡΤΑ ΚΑΙ ΜΗ- ΚΥΡΤΑ, ΓΕΝΙΚΩΣ ΜΗ-ΔΙΑΦΟΡΙΣΙΜΑ ΥΠΕΡΔΥΝΑΜΙΚΑ ΜΕ ΤΗΝ ΒΟΗΘΕΙΑ ΓΕΝΙΚΕΥΣΕΩΝΤΗΣ ΕΝΝΟΙΑΣ ΤΟΥ ΔΙΑΦΟΡΙΚΟΥ ΤΗΣ ΛΕΙΑΣ ΑΝΑΛΥΣΕΩΣ: Ο ΥΠΟΔΙΑΦΟΡΙΚΟΣ ΤΕΛΕΣΤΗΣ ΤΗΣ ΚΥΡΤΗΣ ΑΝΑΛΥΣΕΩΣ ΚΑΤΑ J.J. MOREAU ΧΡΗΣΙΜΟΠΟΙΕΙΤΑΙ ΓΙΑ ΜΟΝΟΤΟΝΟΥΣ ΝΟΜΟΥΣ, Ο ΓΕΝΙΚΕΥΜΕΝΟΣ ΥΠΟΔΙΑΦΟΡΙΚΟΣ ΤΕΛΕΣΤΗΣ ΚΑΤΑ F.H. CLARKE ΚΑΙ Ο ΓΕΝΙΚΕΥΜΕΝΟΣ ΔΙΑΦΟΡΙΚΟΣ ΤΕΛΕΣΤΗΣ (QUASIDIFFERENTIAL) ΚΑΤΑ V.F. DEM'YANOV ΧΡΗΣΙΜΟΠΟΙΟΥΝΤΑΙ ΓΙΑ ΜΗ-ΜΟΝΟΤΟΝΟΥΣ ΝΟΜΟΥΣ. ΤΟ ΠΡΟΒΛΗΜΑ ΣΤΑΤΙΚΟΥ ΥΠΟΛΟΓΙΣΜΟΥ ΤΟΥ ΦΟΡΕΑ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ ΓΡΑΦΕΤΑΙΣΤΗΝ ΓΕΝΙΚΗ ΜΟΡΦΗ ΠΡΟΒΛΗΜΑΤΟΣ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ ΚΑΙ ΣΥΣΤΗΜΑΤΟΣΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ, ΑΝΑΛΟΓΑ ΜΕ ΤΙΣ ΥΠΟΘΕΣΕΙΣ ΠΟΥ ΓΙΝΟΝΤΑΙ ΣΧΕΤΙΚΑ ΜΕ ΤΗΝ ΜΟΡΦΗ ΤΩΝ ΝΟΜΩΝ ΤΗΣ ΔΙΕΠΙΦΑΝΕΙΑΣ. Η ΥΠΑΡΞΗ ΚΑΙ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΕΩΣ ΚΑΘΩΣ ΚΑΙ…

Subjects/Keywords: COMPOSITE MATERIALS-STRUCTURES; Finite element analysis; INEQUALITY PROBLEMS IN MECHANICS; NONSMOOTH ANALYSIS: APPLICATIONS; STATICS OF MONUMENTS-MASONRY STRUCTURES; STRUCTURAL ANALYSIS: INTERFACES; UNILATERAL CONTACT-FRICTION PROBLEMS; VARIATIONAL PROBLEMS IN MECHANICS; VARIATIONAL-HEMIVARIATIONAL INEQUALITIES; ΑΝΙΣΟΤΗΤΕΣ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ; ΑΝΙΣΟΤΙΚΑ ΠΡΟΒΛΗΜΑΤΑ ΜΗΧΑΝΙΚΗΣ; ΜΗ-ΓΡΑΜΜΙΚΗ ΑΝΑΛΥΣΗ ΦΟΡΕΩΝ: ΜΟΡΦΩΣΗ, ΑΛΓΟΡΙΘΜΟΙ; ΜΗ-ΛΕΙΑ ΑΝΑΛΥΣΗ: ΕΦΑΡΜΟΓΕΣ; ΠΕΠΕΡΑΣΜΕΝΑ ΣΤΟΙΧΕΙΑ: ΥΠΟΛΟΓΙΣΜΟΙ; ΠΡΟΒΛΗΜΑΤΑ ΜΕΤΑΒΟΛΩΝ ΣΤΗΝ ΜΗΧΑΝΙΚΗ; ΠΡΟΒΛΗΜΑΤΑ ΜΟΝΟΠΛΕΥΡΗΣ ΕΠΑΦΗΣ-ΤΡΙΒΗΣ; ΣΤΑΤΙΚΗ ΜΕΛΕΤΗ ΦΟΡΕΩΝ, ΔΙΕΠΙΦΑΝΕΙΕΣ; ΣΤΑΤΙΚΗ ΤΩΝ ΜΝΗΜΕΙΩΝ-ΠΟΛΥΤΜΗΜΑΤΙΚΩΝ ΦΟΡΕΩΝ; ΣΥΝΘΕΤΑ ΥΛΙΚΑ-ΦΟΡΕΙΣ

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APA (6^th Edition):

ΣΤΑΥΡΟΥΛΑΚΗΣ, �. (1991). ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ. (Thesis). Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); Aristotle University Of Thessaloniki (AUTH). Retrieved from http://hdl.handle.net/10442/hedi/1628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

ΣΤΑΥΡΟΥΛΑΚΗΣ, ΓΕΩΡΓΙΟΣ. “ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ.” 1991. Thesis, Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); Aristotle University Of Thessaloniki (AUTH). Accessed March 06, 2021. http://hdl.handle.net/10442/hedi/1628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

ΣΤΑΥΡΟΥΛΑΚΗΣ, ΓΕΩΡΓΙΟΣ. “ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ.” 1991. Web. 06 Mar 2021.

Vancouver:

ΣΤΑΥΡΟΥΛΑΚΗΣ �. ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ. [Internet] [Thesis]. Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); Aristotle University Of Thessaloniki (AUTH); 1991. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10442/hedi/1628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

ΣΤΑΥΡΟΥΛΑΚΗΣ �. ΥΠΟΛΟΓΙΣΜΟΣ ΦΟΡΕΩΝ ΜΕ ΔΙΕΠΙΦΑΝΕΙΕΣ. ΜΟΡΦΩΣΗ ΚΑΙ ΜΕΛΕΤΗ ΠΡΟΒΛΗΜΑΤΩΝ ΑΝΙΣΟΤΗΤΩΝ ΜΕΤΑΒΟΛΩΝ-ΗΜΙΜΕΤΑΒΟΛΩΝ. [Thesis]. Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ); Aristotle University Of Thessaloniki (AUTH); 1991. Available from: http://hdl.handle.net/10442/hedi/1628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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