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