Approximation and Optimization of Discrete and Differential Inclusions

ISBN-10: 0123884284

ISBN-13: 9780123884282

Edition: 2011

Authors: Elimhan Mahmudov

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Description:

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
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Book details

Copyright year: 2011
Publisher: Elsevier
Publication date: 8/25/2011
Binding: Hardcover
Pages: 396
Size: 6.00" wide x 9.00" long x 1.25" tall
Weight: 1.584
Language: English

Dedication
Preface
Acknowledgments
About the Author
Convex Sets and Functions
Introduction
Some basic Properties of Convex Sets
Convex Cones and Dual Cones
The Main Properties of Convex Functions
Conjugate of Convex Function
Directional Derivatives and Subdifferentials
Multivalued Locally Adjoint Mappings
Introduction
Locally Adjoint Mappings to Convex Multivalued Mappings
The Calculus of Locally Adjoint Mappings
Locally Adjoint Mappings in Concrete Cases
Duality Theorems for Convex Multivalued Mappings
Mathematical Programming and Multivalued Mappings
Introduction
Necessary Conditions for an Extremum in Convex Programming Problems
Lagrangian and Duality in Convex Programming Problems
Cone of Tangent Directions and Locally Tents
CUA of Functions
LAM in the Nonconvex Case
Necessary Conditions for an Extremum in Nonconvex Problems
Optimization of Ordinary Discrete and Differential Inclusions and t1-TransversaIity Conditions
Introduction
Optimization of Ordinary Discrete Inclusions
Polyhedral Optimization of Discrete and Differential Inclusions
Polyhedral Adjoint Differential Inclusions and the Finiteness of Switching Number
Bolza Problems for Differential Inclusions with State Constraints
Optimal Control of Hereditary Functional-Differential Inclusions with Varying Time Interval and State Constraints
Optimal Control of HODI of Bolza Type with Varying Time Interval
On Duality of Ordinary Discrete and Differential Inclusions with Convex Structures
Introduction
Duality in Mathematical Programs with Equilibrium Constraints
Duality in Problems Governed by Polyhedral Maps
Duality in Problems Described by Convex Discrete Inclusions
The Main Duality Results in Problems with Convex Differential Inclusions
Optimization of Discrete and Differential Inclusions with Distributed Parameters via Approximation
Introduction
The Optimality Principle of Boundary-Value Problems for Discrete-Approximation and First-Order Partial Differential Inclusions and Duality
Optimal Control of the Cauchy Problem for First-Order Discrete and Partial Differential Inclusions
Optimal Control of Darboux-Type Discrete-Approximation and Differential Inclusions with Set-Valued Boundary Conditions and Duality
Optimal Control of the Elliptic-Type Discrete and Differential Inclusions with Dirichlet and Neumann Boundary Conditions via Approximation
Optimization of Discrete-Approximation and Differential Inclusions of Parabolic Type and Duality
Optimization of the First Boundary Value Problem for Hyperbolic-Type Diascrete-Approximation and Differential Inclusions
References
Glossary of Notations
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