Dedication
Preface
Acknowledgments
About the Author
1Convex Sets and Functions
1.1Introduction
1.2Some Basic Properties of Convex Sets
1.3Convex Cones and Dual Cones
1.4The Main Properties of Convex Functions
1.5Conjugate of Convex Function
1.6Directional Derivatives and Subdifferentials
2Multivalued Locally Adjoint Mappings
2.1Introduction
2.2Locally Adjoint Mappings to Convex Multivalued Mappings
2.3The Calculus of Locally Adjoint Mappings
2.4Locally Adjoint Mappings in Concrete Cases
2.5Duality Theorems for Convex Multivalued Mappings
3Mathematical Programming and Multivalued Mappings
3.1Introduction
3.2Necessary Conditions for an Extremum in Convex Programming Problems
3.3Lagrangian and Duality in Convex Programming Problems
3.4Cone of Tangent Directions and Locally Tents
3.5CUA of Functions
3.6LAM in the Nonconvex Case
3.7Necessary Conditions for an Extremum in Nonconvex Problems
4Optimization of Ordinary Discrete and Differential Inclusions and t1-Trausversality Conditions
4.1Introduction
4.2Optimization of Ordinary Discrete Inclusions
4.3Polyhedral Optimization of Discrete and Differential Inclusions
4.4Polyhedral Adjoint Differential Inclusions and the Finiteness of Switching Numbers
4.5Bolza Problems for Differential Inclusions with State Constraints
4.6Optimal Control of Hereditary Functional-Differential Inclusions with Varying Time Interval and State Constraints
4.7Optimal Control of HODI of Bolza Type with Varying Time Interval
5On Duality of Ordinary Discrete and Differential Inclusions with Convex Structures
5.1Introduction
5.2Duality in Mathematical Programs with Equilibrium Constraints
5.3Duality in Problems Governed by Polyhedral Maps
5.4Duality in Problems Described by Convex Discrete Inclusions
5.5The Main Duality Results in Problems with Convex Differential Inclusions
6Optimization of Discrete and Differential Inclusions with
Distributed Parameters via Approximation
6.1Introduction
6.2The Optimality Principle of Boundary-Value Problems for Discrete-Approximation and First-Order Partial Differential Inclusions and Duality
6.3Optimal Control of the Cauchy Problem for First-Order Discrete and Partial Differential Inclusions
6.4Optimal Control of Darboux-Type Discrete-Approximation and Differential Inclusions with Set-Valued Boundary Conditions and Duality
6.5Optimal Control of the Elliptic-Type Discrete and Differential Inclusions with Dirichlet and Neumann Boundary Conditions via Approximation
6.6Optimization of Discrete-Approximation and Differential Inclusions of Parabolic Type and Duality
6.7Optimization of the First Boundary Value Problem for Hyperbolic-Type Discrete-Approximation and Differential Inclusions
References
Glossary of Notations
