Title Optimization : algorithms and consistent approximations / Elijah Polak

Published New York : Springer-Verlag, [1997] ©1997

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Location	Call no.	Vol.	Availability
W'PONDS	519.3 Pol/Oaa		AVAILABLE

Description xx, 779 pages ; 24 cm Series Applied mathematical sciences ; 124 Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 124 Contents 1. Unconstrained Optimization. 1.1. Optimality Conditions. 1.2. Algorithm Models and Convergence Conditions I. 1.3. Gradient Methods. 1.4. Newton's Method. 1.5. Methods of Conjugate Directions. 1.6. Quasi-Newton Methods. 1.7. One-Dimensional Optimization. 1.8. Newton's Method for Equations and Inequalities -- 2. Finite Min-Max and Constrained Optimization. 2.1. Optimality Conditions for Min-Max. 2.2. Optimality Conditions for Constrained Optimization. 2.3. Algorithm Models and Convergence Conditions II. 2.4. First-Order Min-Max Algorithms. 2.5. Newton's Method for Min-Max Problems. 2.6. Phase I - Phase II Methods of Centers. 2.7. Penalty Function Algorithms. 2.8. Augmented Lagrangian Methods. 2.9. Sequential Quadratic Programming -- 3. Semi-Infinite Optimization. 3.1. Optimality Conditions for Semi-Infinite Min-Max. 3.2. Optimality Conditions for Constrained Semi-Infinite Optimization. 3.3. Theory of Consistent Approximations. 3.4. Semi-Infinite Min-Max Algorithms 3.5. Algorithms for Inequality-Constrained Semi-Infinite Optimization. 3.6. Algorithms for Semi-Infinite Optimization with Mixed Constraints -- 4. Optimal Control. 4.1. Canonical Forms of Optimal Control Problems. 4.2. Optimality Conditions for Optimal Control. 4.3. Algorithms for Unconstrained Optimal Control. 4.4. Min-Max Algorithms for Optimal Control. 4.5. Algorithms for Problems with State Constraints I: Inequality Constraints. 4.6. Algorithms for Problems with State Constraints II: Equality Constraints. 4.7. Algorithms for Problems with State Constraints III: Equality and Inequality Constraints -- 5. Mathematical Background. 5.1. Results from Functional Analysis. 5.2. Convex Sets and Convex Functions. 5.3. Properties of Set-Valued Functions. 5.4. Properties of Max Functions. 5.5. Minimax Theorems. 5.6. Differential Equations Bibliography Includes bibliographical references (pages 743-772) and index Subject Algorithms. Mathematical optimization. LC no. 97002158 ISBN 0387949712 (alk. paper)

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