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You searched for subject:(monotone iterative method). Showing records 1 – 3 of 3 total matches.

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NSYSU

1. Chen, Yen-Ling. Iterative Methods for Minimization Problems over Fixed Point Sets.

Degree: Master, Applied Mathematics, 2011, NSYSU

In this paper we study through iterative methods the minimization problem minx∈C Î(x) (P) where the set C of constraints is the set of fixed points of a nonexpansive mapping T in a real Hilbert space H, and the objective function Î:HâR is supposed to be continuously Gateaux dierentiable. The gradient projection method for solving problem (P) involves with the projection PC. When C = Fix(T), we provide a so-called hybrid iterative method for solving (P) and the method involves with the mapping T only. Two special cases are included: (1) Î(x)=(1/2)||x-u||2 and (2) Î(x)=<Ax,x> - <x,b>. The first case corresponds to finding a fixed point of T which is closest to u from the fixed point set Fix(T). Both cases have received a lot of investigations recently. Advisors/Committee Members: Jen-Chih Yao (chair), Ngai-Ching Wong (chair), Hong-Kun Xu (committee member), Lai-Jiu Lin (chair).

Subjects/Keywords: Halpern's algorithm; demiclosedness principle; hybrid method; quadratic optimization; strongly monotone; monotone mapping; projection; iterative method; fixed point; nonexpansive mapping; Minimization

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

APA (6th Edition):

Chen, Y. (2011). Iterative Methods for Minimization Problems over Fixed Point Sets. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0602111-000058

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

Chicago Manual of Style (16th Edition):

Chen, Yen-Ling. “Iterative Methods for Minimization Problems over Fixed Point Sets.” 2011. Thesis, NSYSU. Accessed January 20, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0602111-000058.

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

MLA Handbook (7th Edition):

Chen, Yen-Ling. “Iterative Methods for Minimization Problems over Fixed Point Sets.” 2011. Web. 20 Jan 2021.

Vancouver:

Chen Y. Iterative Methods for Minimization Problems over Fixed Point Sets. [Internet] [Thesis]. NSYSU; 2011. [cited 2021 Jan 20]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0602111-000058.

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

Council of Science Editors:

Chen Y. Iterative Methods for Minimization Problems over Fixed Point Sets. [Thesis]. NSYSU; 2011. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0602111-000058

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

2. Nagesseur, Ludovic. Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions.

Degree: Docteur es, Mathématiques appliquées et applications mathématiques, 2012, Université des Antilles et de la Guyane

Cette thèse est consacrée à la résolution d'un problème fondamental de l'analyse variationnelle qu'est la recherchede zéros d'opérateurs maximaux monotones dans un espace de Hilbert. Nous nous sommes tout d'abord intéressés au cas de l'opérateur somme étendue de deux opérateurs maximaux monotones; la recherche d'un zéro de cet opérateur est un problème dont la bibliographie est peu fournie: nous proposons une version modifiée de l'algorithme d'éclatement forward-backward utilisant à chaque itération, l'epsilon-élargissement d'un opérateur maximal monotone,afin de construire une solution. Nous avons ensuite étudié la convergence d'un nouvel algorithme de faisceaux pour construire ID zéro d'un opérateur maximal monotone quelconque en dimension finie. Cet algorithme fait intervenir une double approximation polyédrale de l'epsilon-élargissement de l'opérateur considéré

This thesis is devoted to solving a basic problem of variational analysis which is the search of zeros of maximal monotone operators in a Hilbert space. First of aIl, we concentrate on the case of the extended som of two maximal monotone operators; the search of a zero of this operator is a problem for which the bibliography is not abondant: we purpose a modified version of the forward-backward splitting algorithm using at each iteration, the epsilon-enlargement of a maximal monotone operator, in order to construet a solution. Secondly, we study the convergence of a new bondie algorithm to construet a zero of an arbitrary maximal monotone operator in a finite dimensional space. In this algorithm, intervenes a double polyhedral approximation of the epsilon-enlargement of the considered operator

Advisors/Committee Members: Lassonde, Marc (thesis director).

Subjects/Keywords: Analyse convexe et variationnelle; Inéquation variationnelle; Méthode itérative; Opérateur maximal monotone; Convex and Variational Analysis; Variational equation; Iterative method; Maximal monotone operator

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

APA (6th Edition):

Nagesseur, L. (2012). Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions. (Doctoral Dissertation). Université des Antilles et de la Guyane. Retrieved from http://www.theses.fr/2012AGUY0548

Chicago Manual of Style (16th Edition):

Nagesseur, Ludovic. “Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions.” 2012. Doctoral Dissertation, Université des Antilles et de la Guyane. Accessed January 20, 2021. http://www.theses.fr/2012AGUY0548.

MLA Handbook (7th Edition):

Nagesseur, Ludovic. “Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions.” 2012. Web. 20 Jan 2021.

Vancouver:

Nagesseur L. Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions. [Internet] [Doctoral dissertation]. Université des Antilles et de la Guyane; 2012. [cited 2021 Jan 20]. Available from: http://www.theses.fr/2012AGUY0548.

Council of Science Editors:

Nagesseur L. Utilisation de l'élargissement d'opérateurs maximaux monotones pour la résolution d'inclusions variationnelles : Using the expansion of maximal monotone operators for solving variational inclusions. [Doctoral Dissertation]. Université des Antilles et de la Guyane; 2012. Available from: http://www.theses.fr/2012AGUY0548


Brno University of Technology

3. Vážanová, Gabriela. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.

Degree: 2020, Brno University of Technology

This thesis focuses on functional differential equations of mixed type also referred to as advance-delay equations. It gives sufficient conditions for the existence of global and semi-global solutions to nonlinear mixed differential systems. The methods used in this thesis consist of building suitable operators for differential equations and proving the existence of their fixed points. These fixed points are then used to construct the solutions of advance-delay equations. The monotone iterative method and Schauder-Tychonoff fixed point theorems are used in the proofs. In both cases, we also provide solution estimates. Moreover, with the monotone iterative method, these estimates may be improved by iterations. In addition, criteria for linear equations and systems are derived and series of examples are provided. The results obtained are also applicable to ordinary, delayed or advanced differential equations. Advisors/Committee Members: Diblík, Josef (advisor), Růžičková, Miroslava (referee), Fečkan,, Michal (referee).

Subjects/Keywords: funkcionální diferenciální rovnice smíšeného typu; zpožděný argument; předcházející argument; semi-globální řešení; globální řešení; monotónní iterační metoda; Schauderova-Tychonovova věta o pevném bodu; mixed-type functional differential equation; delayed argument; advanced argument; semi-global solution; global solution; monotone iterative method; Schauder-Tychonoff fixed point theorem

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

APA (6th Edition):

Vážanová, G. (2020). Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/195761

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

Chicago Manual of Style (16th Edition):

Vážanová, Gabriela. “Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.” 2020. Thesis, Brno University of Technology. Accessed January 20, 2021. http://hdl.handle.net/11012/195761.

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

MLA Handbook (7th Edition):

Vážanová, Gabriela. “Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations.” 2020. Web. 20 Jan 2021.

Vancouver:

Vážanová G. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. [Internet] [Thesis]. Brno University of Technology; 2020. [cited 2021 Jan 20]. Available from: http://hdl.handle.net/11012/195761.

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

Council of Science Editors:

Vážanová G. Existence a vlastnosti globálních řešení funkcionálních diferenciálních rovnic smíšeného typu: Existence and Properties of Global Solutions of Mixed-Type Functional Differential Equations. [Thesis]. Brno University of Technology; 2020. Available from: http://hdl.handle.net/11012/195761

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

.