Approximation and optimization of discrete and differential inclusions /
Saved in:
| Author / Creator: | Mahmudov, Elimhan N. |
|---|---|
| Edition: | 1st ed. |
| Imprint: | Waltham, MA : Elsevier, 2011. |
| Description: | xii, 379 p. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8518424 |
Table of Contents:
- Dedication
- Preface
- Acknowledgments
- About the Author
- 1. Convex Sets and Functions
- 1.1. Introduction
- 1.2. Some basic Properties of Convex Sets
- 1.3. Convex Cones and Dual Cones
- 1.4. The Main Properties of Convex Functions
- 1.5. Conjugate of Convex Function
- 1.6. Directional Derivatives and Subdifferentials
- 2. Multivalued Locally Adjoint Mappings
- 2.1. Introduction
- 2.2. Locally Adjoint Mappings to Convex Multivalued Mappings
- 2.3. The Calculus of Locally Adjoint Mappings
- 2.4. Locally Adjoint Mappings in Concrete Cases
- 2.5. Duality Theorems for Convex Multivalued Mappings
- 3. Mathematical Programming and Multivalued Mappings
- 3.1. Introduction
- 3.2. Necessary Conditions for an Extremum in Convex Programming Problems
- 3.3. Lagrangian and Duality in Convex Programming Problems
- 3.4. Cone of Tangent Directions and Locally Tents
- 3.5. CUA of Functions
- 3.6. LAM in the Nonconvex Case
- 3.7. Necessary Conditions for an Extremum in Nonconvex Problems
- 4. Optimization of Ordinary Discrete and Differential Inclusions and t1-TransversaIity Conditions
- 4.1. Introduction
- 4.2. Optimization of Ordinary Discrete Inclusions
- 4.3. Polyhedral Optimization of Discrete and Differential Inclusions
- 4.4. Polyhedral Adjoint Differential Inclusions and the Finiteness of Switching Number
- 4.5. Bolza Problems for Differential Inclusions with State Constraints
- 4.6. Optimal Control of Hereditary Functional-Differential Inclusions with Varying Time Interval and State Constraints
- 4.7. Optimal Control of HODI of Bolza Type with Varying Time Interval
- 5. On Duality of Ordinary Discrete and Differential Inclusions with Convex Structures
- 5.1. Introduction
- 5.2. Duality in Mathematical Programs with Equilibrium Constraints
- 5.3. Duality in Problems Governed by Polyhedral Maps
- 5.4. Duality in Problems Described by Convex Discrete Inclusions
- 5.5. The Main Duality Results in Problems with Convex Differential Inclusions
- 6. Optimization of Discrete and Differential Inclusions with Distributed Parameters via Approximation
- 6.1. Introduction
- 6.2. The Optimality Principle of Boundary-Value Problems for Discrete-Approximation and First-Order Partial Differential Inclusions and Duality
- 6.3. Optimal Control of the Cauchy Problem for First-Order Discrete and Partial Differential Inclusions
- 6.4. Optimal Control of Darboux-Type Discrete-Approximation and Differential Inclusions with Set-Valued Boundary Conditions and Duality
- 6.5. Optimal Control of the Elliptic-Type Discrete and Differential Inclusions with Dirichlet and Neumann Boundary Conditions via Approximation
- 6.6. Optimization of Discrete-Approximation and Differential Inclusions of Parabolic Type and Duality
- 6.7. Optimization of the First Boundary Value Problem for Hyperbolic-Type Diascrete-Approximation and Differential Inclusions
- References
- Glossary of Notations
