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Analyse convexe et problèmes variationnels / Ivar Ekeland, Roger Temam
| Analyse convexe et problèmes variationnels / Ivar Ekeland, Roger Temam |
| Autore | Ekeland, Ivar |
| Pubbl/distr/stampa | Paris : Dunod, c1974 |
| Descrizione fisica | ix, 340 p. ; 25 cm |
| Disciplina | 515.64 |
| Altri autori (Persone) | Temam, Rogerauthor |
| Collana | Etudes mathématiques |
| Soggetto topico |
Calculus of variations
Convex functions Duality theory Mathematical optimization |
| ISBN | 204007368X |
| Classificazione | AMS 49N15 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | fre |
| Record Nr. | UNISALENTO-991000676689707536 |
Ekeland, Ivar
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| Paris : Dunod, c1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Conjugate duality and optimization / R. Tyrrell Rockafellar
| Conjugate duality and optimization / R. Tyrrell Rockafellar |
| Autore | Rockafellar, R. Tyrrell |
| Pubbl/distr/stampa | Philadelphia : SIAM (Society for Industrial and Applied Mathematics), c1974 |
| Descrizione fisica | vi, 74 p. ; 26 cm. |
| Disciplina | 515.64 |
| Collana | CBMS-NSF Regional conference series in applied mathematics ; 16 |
| Soggetto topico |
Convex functions
Duality theory Mathematical optimization |
| ISBN | 0898710138 |
| Classificazione | AMS 49N15 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000782159707536 |
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Rockafellar, R. Tyrrell
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| Philadelphia : SIAM (Society for Industrial and Applied Mathematics), c1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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CONVEX ANALYSIS
| CONVEX ANALYSIS |
| Autore | KRANTZ STEVEN G |
| Pubbl/distr/stampa | [Place of publication not identified], : CRC Press, 2017 |
| Descrizione fisica | 1 online resource (174 p.) |
| Disciplina | 515/.882 |
| Collana | Textbooks in mathematics |
| Soggetto topico |
Convex functions
Functional analysis |
| ISBN |
0-429-08245-2
1-138-44167-8 1-4987-0638-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front Cover; Dedication; Table of Contents; Preface; Biography of Steven G.Krantz; Chapter 0: Why Convexity?; Chapter 1: Basic Ideas; Chapter 2: Characterization of Convexity Using Functions; Chapter 3: Further Developments Using Functions; Chapter 4: Applications of the Idea of Convexity; Chapter 5: More Sophisticated Ideas; Chapter 6: The MiniMax Theorem; Chapter 7: Concluding Remarks; Appendix: Technical Tools; Table of Notation; Glossary; Bibliography |
| Record Nr. | UNINA-9910787002303321 |
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KRANTZ STEVEN G
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| [Place of publication not identified], : CRC Press, 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Convex analysis
| Convex analysis |
| Autore | Krantz Steven G (Steven George), <1951-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | [Place of publication not identified], : CRC Press, 2017 |
| Descrizione fisica | 1 online resource (174 p.) |
| Disciplina | 515/.882 |
| Collana | Textbooks in mathematics |
| Soggetto topico |
Convex functions
Functional analysis |
| ISBN |
1-04-005380-7
0-429-08245-2 1-138-44167-8 1-4987-0638-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front Cover; Dedication; Table of Contents; Preface; Biography of Steven G.Krantz; Chapter 0: Why Convexity?; Chapter 1: Basic Ideas; Chapter 2: Characterization of Convexity Using Functions; Chapter 3: Further Developments Using Functions; Chapter 4: Applications of the Idea of Convexity; Chapter 5: More Sophisticated Ideas; Chapter 6: The MiniMax Theorem; Chapter 7: Concluding Remarks; Appendix: Technical Tools; Table of Notation; Glossary; Bibliography |
| Record Nr. | UNINA-9910828112503321 |
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Krantz Steven G (Steven George), <1951->
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| [Place of publication not identified], : CRC Press, 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Convex analysis / R. Tyrrell Rockafellar
| Convex analysis / R. Tyrrell Rockafellar |
| Autore | Rockafellar, R. Tyrrell |
| Pubbl/distr/stampa | Princeton : Princeton Univ. Press, 1970 |
| Descrizione fisica | xviii, 451 p. ; 23 cm |
| Disciplina | 515.64 |
| Collana | Princeton mathematical series, 0079-5194 ; 28 |
| Soggetto topico | Convex functions |
| ISBN | 0691080690 |
| Classificazione | AMS 52A41 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000791839707536 |
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Rockafellar, R. Tyrrell
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| Princeton : Princeton Univ. Press, 1970 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Convex analysis and beyond . Volume I : basic theory / / Boris S. Mordukhovich and Nguyen Mau Nam
| Convex analysis and beyond . Volume I : basic theory / / Boris S. Mordukhovich and Nguyen Mau Nam |
| Autore | Mordukhovich Boris S. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (597 pages) |
| Disciplina | 516.08 |
| Collana | Springer Series in Operations Research and Financial Engineering |
| Soggetto topico |
Convex geometry
Convex functions Geometria convexa Funcions convexes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-94785-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 FUNDAMENTALS -- 1.1 Topological Spaces -- 1.1.1 Definitions and Examples -- 1.1.2 Topological Interior and Closure of Sets -- 1.1.3 Continuity of Mappings -- 1.1.4 Bases for Topologies -- 1.1.5 Topologies Generated by Families of Mappings -- 1.1.6 Product Topology and Quotient Topology -- 1.1.7 Subspace Topology -- 1.1.8 Separation Axioms -- 1.1.9 Compactness -- 1.1.10 Connectedness and Disconnectedness -- 1.1.11 Net Convergence in Topological Spaces -- 1.2 Topological Vector Spaces -- 1.2.1 Basic Concepts in Topological Vector Spaces -- 1.2.2 Weak Topology and Weak* Topology -- 1.2.3 Quotient Spaces -- 1.3 Some Fundamental Theorems of Functional Analysis -- 1.3.1 Hahn-Banach Extension Theorem -- 1.3.2 Baire Category Theorem -- 1.3.3 Open Mapping Theorem -- 1.3.4 Closed Graph Theorem and Uniform Boundedness Principle -- 1.4 Exercises for Chapter 1 -- 1.5 Commentaries to Chapter 1 -- 2 BASIC THEORY OF CONVEXITY -- 2.1 Convexity of Sets -- 2.1.1 Basic Definitions and Elementary Properties -- 2.1.2 Operations on Convex Sets and Convex Hulls -- 2.2 Cores, Minkowski Functions, and Seminorms -- 2.2.1 Algebraic Interior and Linear Closure -- 2.2.2 Minkowski Gauges -- 2.2.3 Seminorms and Locally Convex Topologies -- 2.3 Convex Separation Theorems -- 2.3.1 Convex Separation in Vector Spaces -- 2.3.2 Convex Separation in Topological Vector Spaces -- 2.3.3 Convex Separation in Finite Dimensions -- 2.3.4 Extreme Points of Convex Sets -- 2.4 Convexity of Functions -- 2.4.1 Descriptions and Properties of Convex Functions -- 2.4.2 Convexity under Differentiability -- 2.4.3 Operations Preserving Convexity of Functions -- 2.4.4 Continuity of Convex Functions -- 2.4.5 Lower Semicontinuity and Convexity -- 2.5 Extended Relative Interiors in Infinite Dimensions -- 2.5.1 Intrinsic Relative and Quasi-Relative Interiors.
2.5.2 Convex Separation via Extended Relative Interiors -- 2.5.3 Extended Relative Interiors of Graphs and Epigraphs -- 2.6 Exercises for Chapter 2 -- 2.7 Commentaries to Chapter 2 -- 3 CONVEX GENERALIZED DIFFERENTIATION -- 3.1 The Normal Cone and Set Extremality -- 3.1.1 Basic Definition and Normal Cone Properties -- 3.1.2 Set Extremality and Convex Extremal Principle -- 3.1.3 Normal Cone Intersection Rule in Topological Vector Spaces -- 3.1.4 Normal Cone Intersection Rule in Finite Dimensions -- 3.2 Coderivatives of Convex-Graph Mappings -- 3.2.1 Coderivative Definition and Elementary Properties -- 3.2.2 Coderivative Calculus in Topological Vector Spaces -- 3.2.3 Coderivative Calculus in Finite Dimensions -- 3.3 Subgradients of Convex Functions -- 3.3.1 Basic Definitions and Examples -- 3.3.2 Subdifferential Sum Rules -- 3.3.3 Subdifferential Chain Rules -- 3.3.4 Subdifferentiation of Maximum Functions -- 3.3.5 Distance Functions and Their Subgradients -- 3.4 Generalized Differentiation under Polyhedrality -- 3.4.1 Polyhedral Convex Separation -- 3.4.2 Polyhedral Normal Cone Intersection Rule -- 3.4.3 Polyhedral Calculus for Coderivatives and Subdifferentials -- 3.5 Exercises for Chapter 3 -- 3.6 Commentaries to Chapter 3 -- 4 ENHANCED CALCULUS AND FENCHEL DUALITY -- 4.1 Fenchel Conjugates -- 4.1.1 Definitions, Examples, and Basic Properties -- 4.1.2 Support Functions -- 4.1.3 Conjugate Calculus -- 4.2 Enhanced Calculus in Banach Spaces -- 4.2.1 Support Functions of Set Intersections -- 4.2.2 Refined Calculus Rules -- 4.3 Directional Derivatives -- 4.3.1 Definitions and Elementary Properties -- 4.3.2 Relationships with Subgradients -- 4.4 Subgradients of Supremum Functions -- 4.4.1 Supremum of Convex Functions -- 4.4.2 Subdifferential Formula for Supremum Functions -- 4.5 Subgradients and Conjugates of Marginal Functions. 4.5.1 Computing Subgradients and Another Chain Rule -- 4.5.2 Conjugate Calculations for Marginal Functions -- 4.6 Fenchel Duality -- 4.6.1 Fenchel Duality for Convex Composite Problems -- 4.6.2 Duality Theorems via Generalized Relative Interiors -- 4.7 Exercises for Chapter 4 -- 4.8 Commentaries to Chapter 4 -- 5 VARIATIONAL TECHNIQUES AND FURTHER SUBGRADIENT STUDY -- 5.1 Variational Principles and Convex Geometry -- 5.1.1 Ekeland's Variational Principle and Related Results -- 5.1.2 Convex Extremal Principles in Banach Spaces -- 5.1.3 Density of ε-Subgradients and Some Consequences -- 5.2 Calculus Rules for ε-Subgradients -- 5.2.1 Exact Sum and Chain Rules for ε-Subgradients -- 5.2.2 Asymptotic ε-Subdifferential Calculus -- 5.3 Mean Value Theorems for Convex Functions -- 5.3.1 Mean Value Theorem for Continuous Functions -- 5.3.2 Approximate Mean Value Theorem -- 5.4 Maximal Monotonicity of Subgradient Mappings -- 5.5 Subdifferential Characterizations of Differentiability -- 5.5.1 Gâteaux and Fréchet Differentiability -- 5.5.2 Characterizations of Gâteaux Differentiability -- 5.5.3 Characterizations of Fréchet Differentiability -- 5.6 Generic Differentiability of Convex Functions -- 5.6.1 Generic Gâteaux Differentiability -- 5.6.2 Generic Fréchet Differentiability -- 5.7 Spectral and Singular Functions in Convex Analysis -- 5.7.1 Von Neumann Trace Inequality -- 5.7.2 Spectral and Symmetric Functions -- 5.7.3 Singular Functions and Their Subgradients -- 5.8 Exercises for Chapter 5 -- 5.9 Commentaries to Chapter 5 -- 6 MISCELLANEOUS TOPICS ON CONVEXITY -- 6.1 Strong Convexity and Strong Smoothness -- 6.1.1 Basic Definitions and Relationships -- 6.1.2 Strong Convexity/Strong Smoothness via Derivatives -- 6.2 Derivatives of Conjugates and Nesterov's Smoothing -- 6.2.1 Differentiability of Conjugate Compositions -- 6.2.2 Nesterov's Smoothing Techniques. 6.3 Convex Sets and Functions at Infinity -- 6.3.1 Horizon Cones and Unboundedness -- 6.3.2 Perspective and Horizon Functions -- 6.4 Signed Distance Functions -- 6.4.1 Basic Definition and Elementary Properties -- 6.4.2 Lipschitz Continuity and Convexity -- 6.5 Minimal Time Functions -- 6.5.1 Minimal Time Functions with Constant Dynamics -- 6.5.2 Subgradients of Minimal Time Functions -- 6.5.3 Signed Minimal Time Functions -- 6.6 Convex Geometry in Finite Dimensions -- 6.6.1 Carathéodory Theorem on Convex Hulls -- 6.6.2 Geometric Version of Farkas Lemma -- 6.6.3 Radon and Helly Theorems on Set Intersections -- 6.7 Approximations of Sets and Geometric Duality -- 6.7.1 Full Duality between Tangent and Normal Cones -- 6.7.2 Tangents and Normals for Polyhedral Sets -- 6.8 Exercises for Chapter 6 -- 6.9 Commentaries to Chapter 6 -- 7 CONVEXIFIED LIPSCHITZIAN ANALYSIS -- 7.1 Generalized Directional Derivatives -- 7.1.1 Definitions and Relationships -- 7.1.2 Properties of Extended Directional Derivatives -- 7.2 Generalized Derivative and Subderivative Calculus -- 7.2.1 Calculus Rules for Subderivatives -- 7.2.2 Calculus of Generalized Directional Derivatives -- 7.3 Directionally Generated Subdifferentials -- 7.3.1 Basic Definitions and Some Properties -- 7.3.2 Calculus Rules for Generalized Gradients -- 7.3.3 Calculus of Contingent Subgradients -- 7.4 Mean Value Theorems and More Calculus -- 7.4.1 Mean Value Theorems for Lipschitzian Functions -- 7.4.2 Additional Calculus Rules for Generalized Gradients -- 7.5 Strict Differentiability and Generalized Gradients -- 7.5.1 Notions of Strict Differentiability -- 7.5.2 Single-Valuedness of Generalized Gradients -- 7.6 Generalized Gradients in Finite Dimensions -- 7.6.1 Rademacher Differentiability Theorem -- 7.6.2 Gradient Representation of Generalized Gradients -- 7.6.3 Generalized Gradients of Antiderivatives. 7.7 Subgradient Analysis of Distance Functions -- 7.7.1 Regular and Limiting Subgradients of Lipschitzian Functions -- 7.7.2 Regular and Limiting Subgradients of Distance Functions -- 7.7.3 Subgradients of Convex Signed Distance Functions -- 7.8 Differences of Convex Functions -- 7.8.1 Continuous DC Functions -- 7.8.2 The Mixing Property of DC Functions -- 7.8.3 Locally DC Functions -- 7.8.4 Subgradients and Conjugates of DC Functions -- 7.9 Exercises for Chapter 7 -- 7.10 Commentaries to Chapter 7 -- Glossary of Notation and Acronyms -- Glossary of Notation and Acronyms -- List of Figures -- References -- -- Subject Index -- Index. |
| Record Nr. | UNINA-9910564678903321 |
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Mordukhovich Boris S.
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| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convex analysis and beyond . Volume I : basic theory / / Boris S. Mordukhovich and Nguyen Mau Nam
| Convex analysis and beyond . Volume I : basic theory / / Boris S. Mordukhovich and Nguyen Mau Nam |
| Autore | Mordukhovich Boris S. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (597 pages) |
| Disciplina | 516.08 |
| Collana | Springer Series in Operations Research and Financial Engineering |
| Soggetto topico |
Convex geometry
Convex functions Geometria convexa Funcions convexes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-94785-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 FUNDAMENTALS -- 1.1 Topological Spaces -- 1.1.1 Definitions and Examples -- 1.1.2 Topological Interior and Closure of Sets -- 1.1.3 Continuity of Mappings -- 1.1.4 Bases for Topologies -- 1.1.5 Topologies Generated by Families of Mappings -- 1.1.6 Product Topology and Quotient Topology -- 1.1.7 Subspace Topology -- 1.1.8 Separation Axioms -- 1.1.9 Compactness -- 1.1.10 Connectedness and Disconnectedness -- 1.1.11 Net Convergence in Topological Spaces -- 1.2 Topological Vector Spaces -- 1.2.1 Basic Concepts in Topological Vector Spaces -- 1.2.2 Weak Topology and Weak* Topology -- 1.2.3 Quotient Spaces -- 1.3 Some Fundamental Theorems of Functional Analysis -- 1.3.1 Hahn-Banach Extension Theorem -- 1.3.2 Baire Category Theorem -- 1.3.3 Open Mapping Theorem -- 1.3.4 Closed Graph Theorem and Uniform Boundedness Principle -- 1.4 Exercises for Chapter 1 -- 1.5 Commentaries to Chapter 1 -- 2 BASIC THEORY OF CONVEXITY -- 2.1 Convexity of Sets -- 2.1.1 Basic Definitions and Elementary Properties -- 2.1.2 Operations on Convex Sets and Convex Hulls -- 2.2 Cores, Minkowski Functions, and Seminorms -- 2.2.1 Algebraic Interior and Linear Closure -- 2.2.2 Minkowski Gauges -- 2.2.3 Seminorms and Locally Convex Topologies -- 2.3 Convex Separation Theorems -- 2.3.1 Convex Separation in Vector Spaces -- 2.3.2 Convex Separation in Topological Vector Spaces -- 2.3.3 Convex Separation in Finite Dimensions -- 2.3.4 Extreme Points of Convex Sets -- 2.4 Convexity of Functions -- 2.4.1 Descriptions and Properties of Convex Functions -- 2.4.2 Convexity under Differentiability -- 2.4.3 Operations Preserving Convexity of Functions -- 2.4.4 Continuity of Convex Functions -- 2.4.5 Lower Semicontinuity and Convexity -- 2.5 Extended Relative Interiors in Infinite Dimensions -- 2.5.1 Intrinsic Relative and Quasi-Relative Interiors.
2.5.2 Convex Separation via Extended Relative Interiors -- 2.5.3 Extended Relative Interiors of Graphs and Epigraphs -- 2.6 Exercises for Chapter 2 -- 2.7 Commentaries to Chapter 2 -- 3 CONVEX GENERALIZED DIFFERENTIATION -- 3.1 The Normal Cone and Set Extremality -- 3.1.1 Basic Definition and Normal Cone Properties -- 3.1.2 Set Extremality and Convex Extremal Principle -- 3.1.3 Normal Cone Intersection Rule in Topological Vector Spaces -- 3.1.4 Normal Cone Intersection Rule in Finite Dimensions -- 3.2 Coderivatives of Convex-Graph Mappings -- 3.2.1 Coderivative Definition and Elementary Properties -- 3.2.2 Coderivative Calculus in Topological Vector Spaces -- 3.2.3 Coderivative Calculus in Finite Dimensions -- 3.3 Subgradients of Convex Functions -- 3.3.1 Basic Definitions and Examples -- 3.3.2 Subdifferential Sum Rules -- 3.3.3 Subdifferential Chain Rules -- 3.3.4 Subdifferentiation of Maximum Functions -- 3.3.5 Distance Functions and Their Subgradients -- 3.4 Generalized Differentiation under Polyhedrality -- 3.4.1 Polyhedral Convex Separation -- 3.4.2 Polyhedral Normal Cone Intersection Rule -- 3.4.3 Polyhedral Calculus for Coderivatives and Subdifferentials -- 3.5 Exercises for Chapter 3 -- 3.6 Commentaries to Chapter 3 -- 4 ENHANCED CALCULUS AND FENCHEL DUALITY -- 4.1 Fenchel Conjugates -- 4.1.1 Definitions, Examples, and Basic Properties -- 4.1.2 Support Functions -- 4.1.3 Conjugate Calculus -- 4.2 Enhanced Calculus in Banach Spaces -- 4.2.1 Support Functions of Set Intersections -- 4.2.2 Refined Calculus Rules -- 4.3 Directional Derivatives -- 4.3.1 Definitions and Elementary Properties -- 4.3.2 Relationships with Subgradients -- 4.4 Subgradients of Supremum Functions -- 4.4.1 Supremum of Convex Functions -- 4.4.2 Subdifferential Formula for Supremum Functions -- 4.5 Subgradients and Conjugates of Marginal Functions. 4.5.1 Computing Subgradients and Another Chain Rule -- 4.5.2 Conjugate Calculations for Marginal Functions -- 4.6 Fenchel Duality -- 4.6.1 Fenchel Duality for Convex Composite Problems -- 4.6.2 Duality Theorems via Generalized Relative Interiors -- 4.7 Exercises for Chapter 4 -- 4.8 Commentaries to Chapter 4 -- 5 VARIATIONAL TECHNIQUES AND FURTHER SUBGRADIENT STUDY -- 5.1 Variational Principles and Convex Geometry -- 5.1.1 Ekeland's Variational Principle and Related Results -- 5.1.2 Convex Extremal Principles in Banach Spaces -- 5.1.3 Density of ε-Subgradients and Some Consequences -- 5.2 Calculus Rules for ε-Subgradients -- 5.2.1 Exact Sum and Chain Rules for ε-Subgradients -- 5.2.2 Asymptotic ε-Subdifferential Calculus -- 5.3 Mean Value Theorems for Convex Functions -- 5.3.1 Mean Value Theorem for Continuous Functions -- 5.3.2 Approximate Mean Value Theorem -- 5.4 Maximal Monotonicity of Subgradient Mappings -- 5.5 Subdifferential Characterizations of Differentiability -- 5.5.1 Gâteaux and Fréchet Differentiability -- 5.5.2 Characterizations of Gâteaux Differentiability -- 5.5.3 Characterizations of Fréchet Differentiability -- 5.6 Generic Differentiability of Convex Functions -- 5.6.1 Generic Gâteaux Differentiability -- 5.6.2 Generic Fréchet Differentiability -- 5.7 Spectral and Singular Functions in Convex Analysis -- 5.7.1 Von Neumann Trace Inequality -- 5.7.2 Spectral and Symmetric Functions -- 5.7.3 Singular Functions and Their Subgradients -- 5.8 Exercises for Chapter 5 -- 5.9 Commentaries to Chapter 5 -- 6 MISCELLANEOUS TOPICS ON CONVEXITY -- 6.1 Strong Convexity and Strong Smoothness -- 6.1.1 Basic Definitions and Relationships -- 6.1.2 Strong Convexity/Strong Smoothness via Derivatives -- 6.2 Derivatives of Conjugates and Nesterov's Smoothing -- 6.2.1 Differentiability of Conjugate Compositions -- 6.2.2 Nesterov's Smoothing Techniques. 6.3 Convex Sets and Functions at Infinity -- 6.3.1 Horizon Cones and Unboundedness -- 6.3.2 Perspective and Horizon Functions -- 6.4 Signed Distance Functions -- 6.4.1 Basic Definition and Elementary Properties -- 6.4.2 Lipschitz Continuity and Convexity -- 6.5 Minimal Time Functions -- 6.5.1 Minimal Time Functions with Constant Dynamics -- 6.5.2 Subgradients of Minimal Time Functions -- 6.5.3 Signed Minimal Time Functions -- 6.6 Convex Geometry in Finite Dimensions -- 6.6.1 Carathéodory Theorem on Convex Hulls -- 6.6.2 Geometric Version of Farkas Lemma -- 6.6.3 Radon and Helly Theorems on Set Intersections -- 6.7 Approximations of Sets and Geometric Duality -- 6.7.1 Full Duality between Tangent and Normal Cones -- 6.7.2 Tangents and Normals for Polyhedral Sets -- 6.8 Exercises for Chapter 6 -- 6.9 Commentaries to Chapter 6 -- 7 CONVEXIFIED LIPSCHITZIAN ANALYSIS -- 7.1 Generalized Directional Derivatives -- 7.1.1 Definitions and Relationships -- 7.1.2 Properties of Extended Directional Derivatives -- 7.2 Generalized Derivative and Subderivative Calculus -- 7.2.1 Calculus Rules for Subderivatives -- 7.2.2 Calculus of Generalized Directional Derivatives -- 7.3 Directionally Generated Subdifferentials -- 7.3.1 Basic Definitions and Some Properties -- 7.3.2 Calculus Rules for Generalized Gradients -- 7.3.3 Calculus of Contingent Subgradients -- 7.4 Mean Value Theorems and More Calculus -- 7.4.1 Mean Value Theorems for Lipschitzian Functions -- 7.4.2 Additional Calculus Rules for Generalized Gradients -- 7.5 Strict Differentiability and Generalized Gradients -- 7.5.1 Notions of Strict Differentiability -- 7.5.2 Single-Valuedness of Generalized Gradients -- 7.6 Generalized Gradients in Finite Dimensions -- 7.6.1 Rademacher Differentiability Theorem -- 7.6.2 Gradient Representation of Generalized Gradients -- 7.6.3 Generalized Gradients of Antiderivatives. 7.7 Subgradient Analysis of Distance Functions -- 7.7.1 Regular and Limiting Subgradients of Lipschitzian Functions -- 7.7.2 Regular and Limiting Subgradients of Distance Functions -- 7.7.3 Subgradients of Convex Signed Distance Functions -- 7.8 Differences of Convex Functions -- 7.8.1 Continuous DC Functions -- 7.8.2 The Mixing Property of DC Functions -- 7.8.3 Locally DC Functions -- 7.8.4 Subgradients and Conjugates of DC Functions -- 7.9 Exercises for Chapter 7 -- 7.10 Commentaries to Chapter 7 -- Glossary of Notation and Acronyms -- Glossary of Notation and Acronyms -- List of Figures -- References -- -- Subject Index -- Index. |
| Record Nr. | UNISA-996472037403316 |
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Mordukhovich Boris S.
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| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Convex analysis and measurable multifunctions / / C. Castaing, M. Valadier
| Convex analysis and measurable multifunctions / / C. Castaing, M. Valadier |
| Autore | Castaing Charles <1932-> |
| Edizione | [1st ed. 1977.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg : , : Springer-Verlag, , [1977] |
| Descrizione fisica | 1 online resource (X, 286 p.) |
| Disciplina | 515.8 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Convex functions
Functional analysis |
| ISBN | 3-540-37384-5 |
| Classificazione |
28A20
26B25 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Convex functions -- Hausdorff distance and Hausdorff uniformity -- Measurable multifunctions -- Topological property of the profile of a measurable multifunction with compact convex values -- Compactness theorems of measurable selections and integral representation theorem -- Primitive of multifunctions and multivalued differential equations -- Convex integrand on locally convex spaces. And its applications -- A natural supplement of L? in the dual of L?. Applications. |
| Record Nr. | UNISA-996466656903316 |
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Castaing Charles <1932->
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| Berlin ; ; Heidelberg : , : Springer-Verlag, , [1977] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Convex analysis and measurable multifunctions / C. Castaing, M. Valadier
| Convex analysis and measurable multifunctions / C. Castaing, M. Valadier |
| Autore | Castaing, Charles |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1977 |
| Descrizione fisica | vii, 278 p. ; 24 cm |
| Disciplina | 515.7 |
| Altri autori (Persone) | Valadier, Michel |
| Collana | Lecture notes in mathematics, 0075-8434 ; 580 |
| Soggetto topico |
Convex functions
Functional analysis |
| ISBN | 3540081445 |
| Classificazione | AMS 52A41 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000792059707536 |
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Castaing, Charles
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| Berlin : Springer-Verlag, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Convex analysis and minimization algorithms / Jean-Baptiste Hiriart-Urruty, Claude Lemarechal
| Convex analysis and minimization algorithms / Jean-Baptiste Hiriart-Urruty, Claude Lemarechal |
| Autore | Hiriart-Urruty, Jean-Baptiste |
| Pubbl/distr/stampa | Berlin ; New York : Springer-Verlag, c1993 |
| Descrizione fisica | 2 v. : ill. ; 24 cm |
| Disciplina | 515.22 |
| Altri autori (Persone) | Lemarechal, Claudeauthor |
| Collana |
Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 305
Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 306 |
| Soggetto topico |
Convex analysis
Convex functions Convex sets Real functions-textbooks |
| ISBN |
3540568506 (v. 1)
3540568522 (v. 2) |
| Classificazione |
AMS 26-01
LC QA331.5.H57 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
V. 1 Fundamentals. - xvii, 417 p.
V. 2. Advanced theory and bundle methods. - xvii, 346 p. |
| Record Nr. | UNISALENTO-991001490629707536 |
|
Hiriart-Urruty, Jean-Baptiste
|
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| Berlin ; New York : Springer-Verlag, c1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Soggetto topico
-
Convex functions
(43)
- Convex sets (10)
- Functional analysis (10)
- Mathematical optimization (9)
- Calculus of variations (4)