UID:
almahu_9947367026602882
Format:
1 online resource (351 p.)
ISBN:
1-282-03502-9
,
9786612035029
,
0-08-096091-X
Series Statement:
Mathematics in science and engineering ; v. 77
Content:
Computational Methods in Optimization
Note:
Includes index.
,
Front Cover; Computational Methods in Optimization: A Unified Approach; Copyright Page; Contents; Preface; Note to the Reader; Conventions and Symbols; CHAPTER 1. PRELIMINARY RESULTS; 1.1 Nonlinear Programming and Optimal Control Problems; 1.2 Optimality Conditions; 1.3 Models and Convergence Conditions for Computational Methods; CHAPTER 2. UNCONSTRAINED MINIMIZATION; 2.1 Gradient and Quasi-Newton Methods in Rn; 2.2 Reduction of Derivative Calculations; 2.3 Conjugate Gradient Methods in Rn; 2.4 Unconstrained Discrete Optimal Control Problems
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2.5 Unconstrained Continuous Optimal Control ProblemsCHAPTER 3. EQUALITY CONSTRAINTS: PROBLEMS ROOT AND BOUNDARY-VALUE; 3.1 Zeros of a Function and Problems with Equality Constraints in Rn; 3.2 Boundary-Value Problems and Discrete Optimal Control; 3.3 Boundary-Value Problems and Continuous Optimal Control; CHAPTER 4. EQUALITY AND INEQUALITY CONSTRAINTS; 4.1 Penalty Function Methods; 4.2 Methods of Centers; 4.3 Methods of Feasible Directions; 4.4 Second-Order Methods of Feasible Directions; 4.5 Gradient Projection Methods; CHAPTER 5. CONVEX CONTROL OPTIMAL PROBLEMS
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5.1 Nonlinear Programming Algorithms Revisited5.2 A Decomposition Algorithm of the Dual Type; 5.3 A Decomposition Algorithm of the Primal Type; CHAPTER 6. RATE OF CONVERGENCE; 6.1 Linear Convergence; 6.2 Superlinear Convergence: Quasi-Newton Methods; 6.3 Superlinear Convergence: Conjugate Gradient Methods; 6.4 Superlinear Convergence: the Variable Metric Algorithm; APPENDIX A: FURTHER MODELS FOR COMPUTATIONAL METHODS; A.1 A Model for the Implementation of Certain Conceptual Optimal Control Algorithms; A.2 An Open-Loop Model for the Implementation of Conceptual Algorithms
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APPENDIX B: PROPERTIES O F CONTINUOUS FUNCTIONSB.1 Expansions of Continuous Functions; B.2 Convex Functions; 8.3. A Few Miscellaneous Results; APPENDIX C: A GUIDE TO IMPLEMENTABLE ALGORITHMS; C.1 General Considerations; C.2 Gradient Methods; C.3 Quasi-Newton Methods; C.4 Conjugate Gradient Algorithms; C.5 Penalty Function Methods; C.6 Methods of Feasible Directions with Linear Search; C.7 Methods of Feasible Directions with Quadratic Search; References; Index; Mathematics in Sciecne and Engineering
,
English
Additional Edition:
ISBN 0-12-559350-3
Language:
English
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