Variational Analysis and Generalized Differentiation II (eBook)

Applications

Boris S. Mordukhovich (Autor)

eBook Download: PDF

2006 | 2006
XXII, 610 Seiten
Springer Berlin (Verlag)
978-3-540-31246-8 (ISBN)

Infos

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces

Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

Ph.D. in Mathematics (1973); distinguished faculty and lifetime scholar of the Academy of Scholars; more than 200 publications (including books and patents); many outstanding research and teaching awards; numerous invited talks to various meetings (e.g., 15 keynote presentations during the last year); organizer of conference, special sessions, and issues of journals; Editorial Boards of 11 international journals; grants and awards from NSF, NATO, NSERC, BSF, Australian Research Council, etc.

Inhalt

Preface 7
Acknowledgments 15
Contents 17
Volume II Applications 24
5 Constrained Optimization and Equilibria 25
5.1 Necessary Conditions in Mathematical Programming 25
5.2 Mathematical Programs with Equilibrium Constraints 68
5.3 Multiobjective Optimization 91
5.4 Subextremality and Suboptimality at Linear Rate 131
5.5 Commentary to Chap. 5 153
6 Optimal Control of Evolution Systems in Banach Spaces 181
6.1 Optimal Control of Discrete-Time and Continuous- time Evolution Inclusions 182
6.2 Necessary Optimality Conditions for Differential Inclusions without Relaxation 232
6.3 Maximum Principle for Continuous-Time Systems with Smooth Dynamics 249
6.4 Approximate Maximum Principle in Optimal Control 270
6.5 Commentary to Chap. 6 319
7 Optimal Control of Distributed Systems 357
7.1 Optimization of Differential-Algebraic Inclusions with Delays 358
7.2 Neumann Boundary Control of Semilinear Constrained Hyperbolic Equations 386
7.3 Dirichlet Boundary Control of Linear Constrained Hyperbolic Equations 408
7.4 Minimax Control of Parabolic Systems with Pointwise State Constraints 420
7.5 Commentary to Chap. 7 461
8 Applications to Economics 483
8.1 Models of Welfare Economics 483
8.2 Second Welfare Theorem for Nonconvex Economies 490
8.3 Nonconvex Economies with Ordered Commodity Spaces 499
8.4 Abstract Versions and Further Extensions 506
8.5 Commentary to Chap. 8 514
References 529
List of Statements 595
Glossary of Notation 617
Subject Index 621

Produkt-Details

• Erscheint lt. Verlag: 2.3.2006
• Reihe/Serie: Grundlehren der mathematischen Wissenschaften
• Reihe/Serie: Grundlehren der mathematischen Wissenschaften
• Zusatzinfo: XXII, 610 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: differential inclusions • Economics • Equilibria • evolution systems • Multi-Objective Optimization • optimal control • Optimization • Partial differential equations
• ISBN-10: 3-540-31246-3 / 3540312463
• ISBN-13: 978-3-540-31246-8 / 9783540312468