subject:(Lipschitz continuous)

1. Rossetto, Diane Rizzotto. Tópicos em métodos ótimos para otimização convexa.

Degree: PhD, Matemática Aplicada, 2012, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27052012-220429/ ;

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Neste trabalho apresentamos um novo método ótimo para otimização de uma função convexa diferenciável sujeita a restrições convexas. Nosso método é baseado em ideias de… (more)

Subjects/Keywords: Convex optimization; gradient Lipschitz continuous.; gradiente Lipschitz contíinuo.; métodos ótimos; optimal methods; Otimização convexa

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

APA (6^th Edition):

Rossetto, D. R. (2012). Tópicos em métodos ótimos para otimização convexa. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27052012-220429/ ;

Chicago Manual of Style (16^th Edition):

Rossetto, Diane Rizzotto. “Tópicos em métodos ótimos para otimização convexa.” 2012. Doctoral Dissertation, University of São Paulo. Accessed February 25, 2021. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27052012-220429/ ;.

MLA Handbook (7^th Edition):

Rossetto, Diane Rizzotto. “Tópicos em métodos ótimos para otimização convexa.” 2012. Web. 25 Feb 2021.

Vancouver:

Rossetto DR. Tópicos em métodos ótimos para otimização convexa. [Internet] [Doctoral dissertation]. University of São Paulo; 2012. [cited 2021 Feb 25]. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27052012-220429/ ;.

Council of Science Editors:

Rossetto DR. Tópicos em métodos ótimos para otimização convexa. [Doctoral Dissertation]. University of São Paulo; 2012. Available from: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27052012-220429/ ;

University of Bath

2. Mawby, Adam D. Integral control of infinite-dimensional linear systems subject to input hysteresis.

Degree: PhD, 2000, University of Bath

URL: https://researchportal.bath.ac.uk/en/studentthesis/integral-control-of-infinitedimensional-linear-systems-subject-to-input-hysteresis(733b8cc0-3725-466a-b710-1a1072ab2be7).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341148

Subjects/Keywords: 510; Continuous time; Discrete; Lipschitz; Dynamic

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

APA (6^th Edition):

Mawby, A. D. (2000). Integral control of infinite-dimensional linear systems subject to input hysteresis. (Doctoral Dissertation). University of Bath. Retrieved from https://researchportal.bath.ac.uk/en/studentthesis/integral-control-of-infinitedimensional-linear-systems-subject-to-input-hysteresis(733b8cc0-3725-466a-b710-1a1072ab2be7).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341148

Chicago Manual of Style (16^th Edition):

Mawby, Adam D. “Integral control of infinite-dimensional linear systems subject to input hysteresis.” 2000. Doctoral Dissertation, University of Bath. Accessed February 25, 2021. https://researchportal.bath.ac.uk/en/studentthesis/integral-control-of-infinitedimensional-linear-systems-subject-to-input-hysteresis(733b8cc0-3725-466a-b710-1a1072ab2be7).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341148.

MLA Handbook (7^th Edition):

Mawby, Adam D. “Integral control of infinite-dimensional linear systems subject to input hysteresis.” 2000. Web. 25 Feb 2021.

Vancouver:

Mawby AD. Integral control of infinite-dimensional linear systems subject to input hysteresis. [Internet] [Doctoral dissertation]. University of Bath; 2000. [cited 2021 Feb 25]. Available from: https://researchportal.bath.ac.uk/en/studentthesis/integral-control-of-infinitedimensional-linear-systems-subject-to-input-hysteresis(733b8cc0-3725-466a-b710-1a1072ab2be7).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341148.

Council of Science Editors:

Mawby AD. Integral control of infinite-dimensional linear systems subject to input hysteresis. [Doctoral Dissertation]. University of Bath; 2000. Available from: https://researchportal.bath.ac.uk/en/studentthesis/integral-control-of-infinitedimensional-linear-systems-subject-to-input-hysteresis(733b8cc0-3725-466a-b710-1a1072ab2be7).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341148

University of North Texas

3. Byrne, Jesse William. Multifractal Analysis of Parabolic Rational Maps.

Degree: 1998, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc278398/

► The investigation of the multifractal spectrum of the equilibrium measure for a parabolic rational map with a Lipschitz continuous potential, φ, which satisfies sup φ… (more)

Subjects/Keywords: multifractals; mathematics; Lipschitz continuous potential; Mappings (Mathematics); Multifractals.

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APA (6^th Edition):

Byrne, J. W. (1998). Multifractal Analysis of Parabolic Rational Maps. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc278398/

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):

Byrne, Jesse William. “Multifractal Analysis of Parabolic Rational Maps.” 1998. Thesis, University of North Texas. Accessed February 25, 2021. https://digital.library.unt.edu/ark:/67531/metadc278398/.

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

MLA Handbook (7^th Edition):

Byrne, Jesse William. “Multifractal Analysis of Parabolic Rational Maps.” 1998. Web. 25 Feb 2021.

Vancouver:

Byrne JW. Multifractal Analysis of Parabolic Rational Maps. [Internet] [Thesis]. University of North Texas; 1998. [cited 2021 Feb 25]. Available from: https://digital.library.unt.edu/ark:/67531/metadc278398/.

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

Council of Science Editors:

Byrne JW. Multifractal Analysis of Parabolic Rational Maps. [Thesis]. University of North Texas; 1998. Available from: https://digital.library.unt.edu/ark:/67531/metadc278398/

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

University of Technology, Sydney

4. Liu, Tongliang. The complexity of algorithmic hypothesis class.

Degree: 2016, University of Technology, Sydney

URL: http://hdl.handle.net/10453/52375

► Statistical learning theory provides the mathematical and theoretical foundations for statistical learning algorithms and inspires the development of more efficient methods. It is observed that… (more)

▼ Statistical learning theory provides the mathematical and theoretical foundations for statistical learning algorithms and inspires the development of more efficient methods. It is observed that learning algorithms may not output some hypotheses in the predefined hypothesis class. Therefore, in this thesis, we focus on statistical learning theory and study how to measure the complexity of the algorithmic hypothesis class, which is a subset of the predefined hypothesis class that a learning algorithm will (or is likely to) output. By designing complexity measures for the algorithmic hypothesis class, we provide new generalization bounds for k-dimensional coding schemes and multi-task learning and propose two frameworks to derive tighter generalization bounds than the current state-of-the-art. We take k-dimensional coding schemes, a set of unsupervised learning algorithms, and multi-task learning, a set of supervised learning algorithms, as examples to demonstrate that learning algorithm outputs may have special properties and are therefore included in a subset of the predefined hypothesis class. By analyzing the subsets (or the algorithmic hypothesis classes), we shed new light on learning problems and derive tighter generalization bounds than the current state-of-the-art. Specifically, for k-dimensional coding schemes, we show that the induced algorithmic loss function classes are sets of Lipschitz-continuous hypotheses and that a dimensionality-dependent complexity measure helps to derive small Lipschitz constants and thus improve the generalization bounds. For multi-task learning, we prove that tasks can act as regularizer and that feature structures can contribute to a small algorithmic hypothesis class and also help to improve the generalization bounds. To more precisely exploit algorithmic hypothesis class complexity by considering the hypothesis and feature structure properties, we extend algorithmic robustness and stability to complexity measures for the hypothesis class. Inspired by the idea of algorithmic robustness, we propose the complexity measure of uniform robustness. Compared to the Rademacher complexity, our measure more finely considers the geometric information of data. For example, when the sample space is covered by a small number of small radius and widely separated balls, the uniform robustness can be very small while the Rademacher complexity can be very large. Moreover, based on the definition of uniform robustness, we also provide a framework to derive generalization bounds for a very general class of learning algorithms. We exploit the algorithmic hypothesis class of stable algorithms by studying the definition of algorithmic stability. Stable learning algorithms have the property that their outputs will not change much when one training example is changed. This implies that their outputs will not be sufficiently far apart, even though the training sample is completely altered. Thus, stable learning algorithms often have small algorithmic hypothesis classes. However, since measuring the…

Subjects/Keywords: Statistical learning theory.; Statistical learning algorithms.; Algorithmic hypothesis class.; K-dimensional coding schemes.; Multi-task learning.; Lipschitz-continuous hypothesis.; Rademacher complexity.; Stable learning algorithms.; Algorithmic Rademacher complexity.

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

APA (6^th Edition):

Liu, T. (2016). The complexity of algorithmic hypothesis class. (Thesis). University of Technology, Sydney. Retrieved from http://hdl.handle.net/10453/52375

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):

Liu, Tongliang. “The complexity of algorithmic hypothesis class.” 2016. Thesis, University of Technology, Sydney. Accessed February 25, 2021. http://hdl.handle.net/10453/52375.

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

MLA Handbook (7^th Edition):

Liu, Tongliang. “The complexity of algorithmic hypothesis class.” 2016. Web. 25 Feb 2021.

Vancouver:

Liu T. The complexity of algorithmic hypothesis class. [Internet] [Thesis]. University of Technology, Sydney; 2016. [cited 2021 Feb 25]. Available from: http://hdl.handle.net/10453/52375.

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

Council of Science Editors:

Liu T. The complexity of algorithmic hypothesis class. [Thesis]. University of Technology, Sydney; 2016. Available from: http://hdl.handle.net/10453/52375

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

5. FENG XIANZHE. NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES.

Degree: 2018, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/144266

Subjects/Keywords: Nonlinear biseparating operators; continuous functions; uniformly continuous functions; Lipschitz functions; differentiable functions; Banach spaces

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

APA (6^th Edition):

XIANZHE, F. (2018). NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/144266

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):

XIANZHE, FENG. “NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES.” 2018. Thesis, National University of Singapore. Accessed February 25, 2021. http://scholarbank.nus.edu.sg/handle/10635/144266.

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

MLA Handbook (7^th Edition):

XIANZHE, FENG. “NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES.” 2018. Web. 25 Feb 2021.

Vancouver:

XIANZHE F. NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES. [Internet] [Thesis]. National University of Singapore; 2018. [cited 2021 Feb 25]. Available from: http://scholarbank.nus.edu.sg/handle/10635/144266.

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

Council of Science Editors:

XIANZHE F. NON-LINEAR BISEPARATING OPERATORS ON VECTOR-VALUED FUNCTION SPACES. [Thesis]. National University of Singapore; 2018. Available from: http://scholarbank.nus.edu.sg/handle/10635/144266

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

6. Gallouët, Thomas. Transport optimal : régularité et applications : Optimal Transport : Regularity and applications.

Degree: Docteur es, Mathématiques, 2012, Lyon, École normale supérieure

URL: http://www.theses.fr/2012ENSL0797

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Cette thèse comporte deux parties distinctes, toutes les deux liées à la théorie du transport optimal. Dans la première partie, nous considérons une variété riemannienne,… (more)

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Cette thèse comporte deux parties distinctes, toutes les deux liées à la théorie du transport optimal. Dans la première partie, nous considérons une variété riemannienne, deux mesures à densité régulière et un coût de transport, typiquement la distance géodésique quadratique et nous nous intéressons à la régularité de l’application de transport optimal. Le critère décisif à cette régularité s’avère être le signe du tenseur de Ma-Trudinger-Wang (MTW). Nous présentons tout d’abord une synthèse des travaux réalisés sur ce tenseur. Nous nous intéressons ensuite au lien entre la géométrie des lieux d’injectivité et le tenseur MTW. Nous montrons que dans de nombreux cas, la positivité du tenseur MTW implique la convexité des lieux d’injectivité. La deuxième partie de cette thèse est liée aux équations aux dérivées partielles. Certaines peuvent être considérées comme des flots gradients dans l’espace de Wasserstein W2. C’est le cas de l’équation de Keller-Segel en dimension 2. Pour cette équation nous nous intéressons au problème de quantification de la masse lors de l’explosion des solutions ; cette explosion apparaît lorsque la masse initiale est supérieure à un seuil critique Mc. Nous cherchons alors à montrer qu’elle consiste en la formation d’un Dirac de masse Mc. Nous considérons ici un modèle particulaire en dimension 1 ayant le même comportement que l’équation de Keller-Segel. Pour ce modèle nous exhibons des bassins d’attractions à l’intérieur desquels l’explosion se produit avec seulement le nombre critique de particules. Finalement nous nous intéressons au profil d’explosion : à l’aide d’un changement d’échelle parabolique nous montrons que la structure de l’explosion correspond aux points critiques d’une certaine fonctionnelle.

This thesis consists in two distinct parts both related to the optimal transport theory.The first part deals with the regularity of the optimal transport map. The key tool is the Ma-Trundinger-Wang tensor and especially its positivity. We first give a review of the known results about the MTW tensor. We then explore the geometrical consequences of the MTW tensor on the injectivity domain. We prove that in many cases the positivity of MTW implies the convexity of the injectivity domain. The second part is devoted to the behaviour of a Keller-Segel solution in the super critical case. In particular we are interested in the mass quantization problem: we wish to quantify the mass aggregated when the blow-up occurs. In order to study the behaviour of the solution we consider a particle approximation of a Keller-Segel type equation in dimension 1. We define this approximation using the gradient flow interpretation of the Keller-Segel equation and the particular structure of the Wasserstein space in dimension 1. We show two kinds of results; we first prove a stability theorem for the blow-up mechanism: we exhibit basins of attraction in which the solution blows up with only the critical number of particles. We then prove a rigidity theorem for the blow-up mechanism: thanks to a parabolic…

Advisors/Committee Members: Villani, Cédric (thesis director).

Subjects/Keywords: Transport optimal; Régularité; Ma-Trundinger-Wang; MTW; Coût; Variété riemannienne; Convexité; Domaine d'injectivité; Lipschitz; C-convexité; Keller-Segel; Quantification de la masse; Particules; 1D; Explosion; Wasserstein; Flot gradient; Espace métrique; Masse critique; Optimal transport; Regularity; Ma-Trundinger-Wang; MTW; Cost; Riemannian manifold; Convexity; Injectivity domain; Lipschitz continuous; C-convexity; Keller-Segel; Mass quantization; Particles; 1D; Blow-up; Wasserstein; Gradient flow; Metric space; Critical mass

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

APA (6^th Edition):

Gallouët, T. (2012). Transport optimal : régularité et applications : Optimal Transport : Regularity and applications. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2012ENSL0797

Chicago Manual of Style (16^th Edition):

Gallouët, Thomas. “Transport optimal : régularité et applications : Optimal Transport : Regularity and applications.” 2012. Doctoral Dissertation, Lyon, École normale supérieure. Accessed February 25, 2021. http://www.theses.fr/2012ENSL0797.

MLA Handbook (7^th Edition):

Gallouët, Thomas. “Transport optimal : régularité et applications : Optimal Transport : Regularity and applications.” 2012. Web. 25 Feb 2021.

Vancouver:

Gallouët T. Transport optimal : régularité et applications : Optimal Transport : Regularity and applications. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2012. [cited 2021 Feb 25]. Available from: http://www.theses.fr/2012ENSL0797.

Council of Science Editors:

Gallouët T. Transport optimal : régularité et applications : Optimal Transport : Regularity and applications. [Doctoral Dissertation]. Lyon, École normale supérieure; 2012. Available from: http://www.theses.fr/2012ENSL0797

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