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.
Author(s): Boris S. Mordukhovich
Edition: 1
Year: 2005
Language: English
Pages: 634
3540254382......Page 1
Contents......Page 16
Volume II Applications......Page 22
5.1 Necessary Conditions in Mathematical Programming......Page 23
5.2 Mathematical Programs with Equilibrium Constraints......Page 66
5.3 Multiobjective Optimization......Page 89
5.4 Subextremality and Suboptimality at Linear Rate......Page 129
5.5 Commentary to Chap. 5......Page 151
6 Optimal Control of Evolution Systems in Banach Spaces......Page 179
6.1 Optimal Control of Discrete-Time and Continuous-time Evolution Inclusions......Page 180
6.2 Necessary Optimality Conditions for Differential Inclusions without Relaxation......Page 230
6.3 Maximum Principle for Continuous-Time Systems with Smooth Dynamics......Page 247
6.4 Approximate Maximum Principle in Optimal Control......Page 268
6.5 Commentary to Chap. 6......Page 317
7 Optimal Control of Distributed Systems......Page 355
7.1 Optimization of Differential-Algebraic Inclusions with Delays......Page 356
7.2 Neumann Boundary Control of Semilinear Constrained Hyperbolic Equations......Page 384
7.3 Dirichlet Boundary Control of Linear Constrained Hyperbolic Equations......Page 406
7.4 Minimax Control of Parabolic Systems with Pointwise State Constraints......Page 418
7.5 Commentary to Chap. 7......Page 459
8.1 Models of Welfare Economics......Page 480
8.2 Second Welfare Theorem for Nonconvex Economies......Page 487
8.3 Nonconvex Economies with Ordered Commodity Spaces......Page 496
8.4 Abstract Versions and Further Extensions......Page 503
8.5 Commentary to Chap. 8......Page 511
References......Page 525
List of Statements......Page 591
Glossary of Notation......Page 612
C......Page 616
D......Page 617
E......Page 618
F......Page 619
I......Page 620
M......Page 621
N......Page 622
P......Page 623
S......Page 624
W......Page 626
Y......Page 627
