Approximation and Optimization of Discrete and Differential Inclusions

by Mahmudov, Elimhan N.

• ISBN13: 9780123884282
• ISBN10: 0123884284
• Format: Hardcover
• Copyright: 2011-08-25
• Publisher: Elsevier Science Ltd

Summary

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Table of Contents

Dedication	p. vii
Preface	p. ix
Acknowledgments	p. xiii
About the Author	p. xv
Convex Sets and Functions	p. 1
Introduction	p. 1
Some basic Properties of Convex Sets	p. 3
Convex Cones and Dual Cones	p. 14
The Main Properties of Convex Functions	p. 25
Conjugate of Convex Function	p. 36
Directional Derivatives and Subdifferentials	p. 41
Multivalued Locally Adjoint Mappings	p. 53
Introduction	p. 53
Locally Adjoint Mappings to Convex Multivalued Mappings	p. 55
The Calculus of Locally Adjoint Mappings	p. 640
Locally Adjoint Mappings in Concrete Cases	p. 72
Duality Theorems for Convex Multivalued Mappings	p. 86
Mathematical Programming and Multivalued Mappings	p. 93
Introduction	p. 93
Necessary Conditions for an Extremum in Convex Programming Problems	p. 97
Lagrangian and Duality in Convex Programming Problems	p. 107
Cone of Tangent Directions and Locally Tents	p. 117
CUA of Functions	p. 122
LAM in the Nonconvex Case	p. 127
Necessary Conditions for an Extremum in Nonconvex Problems	p. 133
Optimization of Ordinary Discrete and Differential Inclusions and t1-TransversaIity Conditions	p. 143
Introduction	p. 143
Optimization of Ordinary Discrete Inclusions	p. 149
Polyhedral Optimization of Discrete and Differential Inclusions	p. 156
Polyhedral Adjoint Differential Inclusions and the Finiteness of Switching Number	p. 170
Bolza Problems for Differential Inclusions with State Constraints	p. 181
Optimal Control of Hereditary Functional-Differential Inclusions with Varying Time Interval and State Constraints	p. 188
Optimal Control of HODI of Bolza Type with Varying Time Interval	p. 206
On Duality of Ordinary Discrete and Differential Inclusions with Convex Structures	p. 217
Introduction	p. 217
Duality in Mathematical Programs with Equilibrium Constraints	p. 219
Duality in Problems Governed by Polyhedral Maps	p. 226
Duality in Problems Described by Convex Discrete Inclusions	p. 235
The Main Duality Results in Problems with Convex Differential Inclusions	p. 245
Optimization of Discrete and Differential Inclusions with Distributed Parameters via Approximation	p. 253
Introduction	p. 253
The Optimality Principle of Boundary-Value Problems for Discrete-Approximation and First-Order Partial Differential Inclusions and Duality	p. 257
Optimal Control of the Cauchy Problem for First-Order Discrete and Partial Differential Inclusions	p. 274
Optimal Control of Darboux-Type Discrete-Approximation and Differential Inclusions with Set-Valued Boundary Conditions and Duality	p. 289
Optimal Control of the Elliptic-Type Discrete and Differential Inclusions with Dirichlet and Neumann Boundary Conditions via Approximation	p. 312
Optimization of Discrete-Approximation and Differential Inclusions of Parabolic Type and Duality	p. 338
Optimization of the First Boundary Value Problem for Hyperbolic-Type Diascrete-Approximation and Differential Inclusions	p. 347
References	p. 365
Glossary of Notations	p. 377
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