Computational methods for optimizing distributed systems, Volume 173 (Mathematics in Science and Engineering)

✍ Scribed by Teo (editor)

• Publisher: Academic Press
• Year: 1984
• Tongue: English
• Leaves: 331
• Category: Library

✦ Table of Contents

Front Cover
Computational Methods for Optimizing Distributed Systems
Copyright Page
Contents
Preface
Chapter I. Mathematical Background
1. Introduction
2. Some Basic Concepts in Functional Analysis
3. Some Basic Concepts in Measure Theory
4. Some Function Spaces
5. Relaxed Controls
6. Multivalued Functions
7. Bibliographical Remarks
Chapter II. Boundary Value Problems of Parabolic Type
1. Introduction
2. Boundary-Value Problems—Basic Definitions and Assumptions
3. Three Elementary Lemmas
4. A Priori Estimates
5. Existence and Uniqueness of Solutions
6. A Continuity Property
7. Certain Properties of Solutions of Equation (2.1)
8. Boundary—Value Problems in General Form
9. A Maximum Principle
Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques
1. Introduction
2. System Description
3. The Optimal Control Problems
4. The Hamiltonian Functions
5. The Successive Controls
6. The Algorithm
7. Necessary and Sufficient Conditions for Optimality
8. Numerical Consideration
9. Examples
10. Discussion
Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques
1. Introduction
2. System Description
3. The Optimization Problem
4. An Increment Formula
5. The Gradient of the Cost Functional
6. A Conditional Gradient Algorithm
7. Numerical Consideration and an Examples
8. Optimal Control Problems with Terminal Inequality Constraints
9. The Finite Element Method
10. Discussion
Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms
1. Introduction
2. The Strong Variational Algorithm
3. The Conditional Gradient Algorithm
4. The Feasible Directions Algorithm
5. Discussion
Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems
1. Introduction
2. The General Problem Statement
3. Preparatory Results
4. A Basic Inequality
5. An Optimal Control Problem with a Linear Cost Functional
6. An Optimal Control Problem with a Linear System
7. The Finite Element Method
8. Discussion
Appendix I: Stochastic Optimal Control Problems
Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V
Appendix III: An Algorithm of Quadratic Programming
Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints
Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter Systems
Appendix VI: Meyer–Polak Proximity Algorithm
References
List of Notation
Index