Variational analysis and applications. (2018)

• Record Type: Book
• Further Information: Note: Boris S. Mordukhovich.
• Authors: Mordukhovich, B. Sh (Boris Sholimovich)
• Contents: Intro; Preface; Contents; 1 Constructions of Generalized Differentiation; 1.1 Normals and Tangents to Closed Sets; 1.1.1 Generalized Normals; 1.1.2 Tangential Preduality; 1.1.3 Smooth Variational Description; 1.2 Coderivatives of Mappings; 1.2.1 Set-Valued Mappings; 1.2.2 Coderivative Definition and Elementary Properties; 1.2.3 Extremal Property of Convex-Valued Multifunctions; 1.3 First-Order Subgradients of Nonsmooth Functions; 1.3.1 Extended-Real-Valued Functions; 1.3.2 Subgradients from Normals to Epigraphs; 1.3.3 Subgradients from Coderivatives 1.3.4 Regular Subgradients and -Enlargements1.3.5 Limiting Subdifferential Representations; 1.3.6 Subgradients of the Distance Function; 1.4 Exercises for Chapter 1; 1.5 Commentaries to Chapter 1; 2 Fundamental Principles of Variational Analysis; 2.1 Extremal Principle for Finite Systems of Sets; 2.1.1 The Concept and Examples of Set Extremality; 2.1.2 Basic Extremal Principle and Some Consequences; 2.2 Extremal Principles for Countable Systems of Sets; 2.2.1 Versions of Extremality for Countable Set Systems; 2.2.2 Conic and Contingent Extremal Principles 2.3 Variational Principles for Functions2.3.1 General Variational Principle; 2.3.2 Applications to Suboptimality and Fixed Points; 2.4 Basic Intersection Rule and Some Consequences; 2.4.1 Normals to Set Intersections and Additions; 2.4.2 Subdifferential Sum Rules; 2.5 Exercises for Chapter 2; 2.6 Commentaries to Chapter 2; 3 Well-Posedness and Coderivative Calculus; 3.1 Well-Posedness Properties of Multifunctions; 3.1.1 Paradigm in Well-Posedness; 3.1.2 Coderivative Characterizations of Well-Posedness; 3.1.3 Characterizations in Special Cases; 3.2 Coderivative Calculus 3.2.1 Coderivative Sum Rules3.2.2 Coderivative Chain Rules; 3.2.3 Other Rules of Coderivative Calculus; 3.3 Coderivative Analysis of Variational Systems; 3.3.1 Parametric Variational Systems; 3.3.2 Coderivative Conditions for Metric Regularity of PVS; 3.3.3 Failure of Metric Regularity for Major Classes of PVS; 3.4 Exercises for Chapter 3; 3.5 Commentaries to Chapter 3; 4 First-Order Subdifferential Calculus; 4.1 Subdifferentiation of Marginal Functions; 4.2 Subdifferentiation of Compositions; 4.3 Subdifferentiation of Minima and Maxima; 4.4 Mean Value Theorems and Some Applications 4.4.1 Mean Value Theorem via Symmetric Subgradients4.4.2 Approximate Mean Value Theorems; 4.4.3 Subdifferential Characterizations from AMVT; 4.5 Exercises for Chapter 4; 4.6 Commentaries to Chapter 4; 5 Coderivatives of Maximal Monotone Operators; 5.1 Coderivative Criteria for Global Monotonicity; 5.1.1 Maximal Monotonicity via Regular Coderivative; 5.1.2 Maximal Monotone Operators with Convex Domains; 5.1.3 Maximal Monotonicity via Limiting Coderivative; 5.2 Coderivative Criteria for Strong Local Monotonicity; 5.2.1 Strong Local Monotonicity and Related Properties
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 515/.64; Mathematics; Calculus of variations; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Calculus of variations; Mathematics; Calculus of Variations and Optimal Control; Optimization; Analysis; Operations Research, Management Science; Mathematics -- Mathematical Analysis; Business & Economics -- Operations Research; Calculus & mathematical analysis; Operational research; Mathematical optimization; Global analysis (Mathematics); Mathematics -- Calculus; Calculus of variations; Electronic books
• Languages: English
• ISBNs: 9783319927756; 3319927752
• Related ISBNs: 9783319927732; 3319927736
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 9, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.