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The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / / David J. Grynkiewicz
| The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / / David J. Grynkiewicz |
| Autore | Grynkiewicz David J. <1978-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (291 pages) |
| Disciplina | 516.08 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Convex geometry
Monoids Geometria convexa Monoides |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031148699
9783031148682 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Convex Geometry -- 1.2 Krull Domains, Transfer Krull Monoids and Factorization -- 1.3 Zero-Sum Sequences -- 1.4 Overview of Main Results -- 2 Preliminaries and General Notation -- 2.1 Convex Geometry -- 2.2 Lattices and Partially Ordered Sets -- 2.3 Sequences and Rational Sequences -- 2.4 Arithmetic Invariants for Transfer Krull Monoids -- 2.5 Asymptotic Notation -- 3 Asymptotically Filtered Sequences, Encasement and Boundedness -- 3.1 Asymptotically Filtered Sequences -- 3.2 Encasement and Boundedness -- 4 Elementary Atoms, Positive Bases and Reay Systems -- 4.1 Basic Non-degeneracy Characterizations -- 4.2 Elementary Atoms and Positive Bases -- 4.3 Reay Systems -- 4.4 -Filtered Sequences, Minimal Encasement and Reay Systems -- 5 Oriented Reay Systems -- 6 Virtual Reay Systems -- 7 Finitary Sets -- 7.1 Core Definitions and Properties -- 7.2 Series Decompositions and Virtualizations -- 7.3 Finiteness Properties of Finitary Sets -- 7.4 Interchangeability and the Structure of X(G0) -- 8 Factorization Theory -- 8.1 Lambert Subsets and Elasticity -- 8.2 The Structure of Atoms and Arithmetic Invariants -- Summary -- 8.3 Transfer Krull Monoids Over Subsets of Finitely Generated Abelian Groups -- Summary -- References -- Index. |
| Record Nr. | UNISA-996495168103316 |
Grynkiewicz David J. <1978->
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / / David J. Grynkiewicz
| The characterization of finite elasticities : factorization theory in Krull monoids via convex geometry / / David J. Grynkiewicz |
| Autore | Grynkiewicz David J. <1978-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (291 pages) |
| Disciplina | 516.08 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Convex geometry
Monoids Geometria convexa Monoides |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031148699
9783031148682 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Convex Geometry -- 1.2 Krull Domains, Transfer Krull Monoids and Factorization -- 1.3 Zero-Sum Sequences -- 1.4 Overview of Main Results -- 2 Preliminaries and General Notation -- 2.1 Convex Geometry -- 2.2 Lattices and Partially Ordered Sets -- 2.3 Sequences and Rational Sequences -- 2.4 Arithmetic Invariants for Transfer Krull Monoids -- 2.5 Asymptotic Notation -- 3 Asymptotically Filtered Sequences, Encasement and Boundedness -- 3.1 Asymptotically Filtered Sequences -- 3.2 Encasement and Boundedness -- 4 Elementary Atoms, Positive Bases and Reay Systems -- 4.1 Basic Non-degeneracy Characterizations -- 4.2 Elementary Atoms and Positive Bases -- 4.3 Reay Systems -- 4.4 -Filtered Sequences, Minimal Encasement and Reay Systems -- 5 Oriented Reay Systems -- 6 Virtual Reay Systems -- 7 Finitary Sets -- 7.1 Core Definitions and Properties -- 7.2 Series Decompositions and Virtualizations -- 7.3 Finiteness Properties of Finitary Sets -- 7.4 Interchangeability and the Structure of X(G0) -- 8 Factorization Theory -- 8.1 Lambert Subsets and Elasticity -- 8.2 The Structure of Atoms and Arithmetic Invariants -- Summary -- 8.3 Transfer Krull Monoids Over Subsets of Finitely Generated Abelian Groups -- Summary -- References -- Index. |
| Record Nr. | UNINA-9910624377103321 |
|
Grynkiewicz David J. <1978->
|
||
| Cham, Switzerland : , : Springer, , [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. | UNINA-9910564678903321 |
|
Mordukhovich Boris S.
|
||
| 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 |
|
Mordukhovich Boris S.
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| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Convex Functions and Their Applications : A Contemporary Approach / / by Constantin P. Niculescu, Lars-Erik Persson
| Convex Functions and Their Applications : A Contemporary Approach / / by Constantin P. Niculescu, Lars-Erik Persson |
| Autore | Niculescu Constantin P |
| Edizione | [3rd ed. 2025.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (949 pages) |
| Disciplina | 515.8 |
| Altri autori (Persone) | PerssonLars-Erik |
| Collana | CMS/CAIMS Books in Mathematics |
| Soggetto topico |
Functions of real variables
Functional analysis Convex geometry Discrete geometry Real Functions Functional Analysis Convex and Discrete Geometry Funcions de variables reals Anàlisi funcional Geometria convexa Geometria discreta |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 9783031719677 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Convex Functions at a First Glance -- More on Convex Functions on Intervals -- Convex Sets in Real Linear Spaces -- Convex Functions on a Normed Linear Space -- Differentiable Convex Functions. 6. Convexity and Majorization -- Convexity in Spaces of Matrices -- Convexity in Spaces of Matrices -- Duality and Convex Optimization -- Special Topics in Majorization Theory. Appendices -- Generalized Convexity on Intervals -- Background on Convex Sets -- Elementary Symmetric Functions -- Second Order Differentiability of Convex Functions -- The Variational Approach of PDE. |
| Record Nr. | UNINA-9910986136003321 |
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Niculescu Constantin P
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Optimization, Discrete Mathematics and Applications to Data Sciences / / edited by Ashkan Nikeghbali, Panos M. Pardalos, Michael Th. Rassias
| Optimization, Discrete Mathematics and Applications to Data Sciences / / edited by Ashkan Nikeghbali, Panos M. Pardalos, Michael Th. Rassias |
| Autore | Nikeghbali Ashkan |
| Edizione | [1st ed. 2025.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
| Descrizione fisica | 1 online resource (361 pages) |
| Disciplina | 519.6 |
| Altri autori (Persone) |
PardalosPanos M
RassiasMichael Th |
| Collana | Springer Optimization and Its Applications |
| Soggetto topico |
Mathematical optimization
Discrete mathematics Number theory System theory Control theory Convex geometry Discrete geometry Optimization Discrete Mathematics Number Theory Systems Theory, Control Convex and Discrete Geometry Optimització matemàtica Matemàtica discreta Teoria de nombres Teoria de sistemes Teoria de control Geometria convexa |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031783692
3031783697 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | On the morphism 1 121, 2 12221 -- Polynomials and combinatorial identities -- Rainbow Greedy Matching Algorithms -- Predictive models of Non-Performing Loans: the case of Greece -- The Cost of Detection in Interaction Testing -- On the study of cycle chains representing non-reversible Markov chains associated with random walks with jumps in fixed environments -- Applying Distance Measures for Discrete Data -- Demand aggregation and mid-term energy planning problem on the business layer -- Factor Fitting, Rank Allocation, and Partitioning in Multilevel Low Rank Matrices -- A Code-based Watermarking Scheme for the Protection of Authenticity of Medical Images -- The minimum cost energy flow problem under demand uncertainty Effect on optimal solution, variability, worst and best case scenarios -- A mathematical study of the Braess’s Paradox within a network comprising four nodes, five edges, and linear time functions -- On similiarities between two global optimization algorithms based on different (Bayesian and Lipschitzian) approaches. |
| Record Nr. | UNINA-9910983040103321 |
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Nikeghbali Ashkan
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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