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Format: 1 online resource (331 p.)

ISBN: 1-282-28902-0 , 9786612289026 , 0-08-095678-5

Series Statement: Mathematics in science and engineering ; v. 173

Content: Computational methods for optimizing distributed systems

Note: Description based upon print version of record. , 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 Problem4. 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. Introduction2. 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 SystemsAppendix VI: Meyer-Polak Proximity Algorithm; References; List of Notation; Index , English

Additional Edition: ISBN 0-12-685480-7

Language: English