Optimization: Algorithms and Consistent Approximations

Hardcover | June 20, 1997

EditorElijah PolakbyE. Polak

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This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework. This book presents the first treatment of optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution.It is also the first to make use of the concepts of epi-convergence and optimality functions in the construction of consistent approximations to infinite dimensional problems.

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This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of c...

Format:HardcoverDimensions:802 pages, 9.25 × 6.1 × 0 inPublished:June 20, 1997Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387949712

ISBN - 13:9780387949710

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Table of Contents

Contents: Unconstrained Optimization.- Optimality Conditions.- Algorithm Models and Convergence Conditions I.- Gradient Methods.- Newton's Method.- Methods of Conjugate Directions.- Quasi-Newton Methods.- One Dimensional Optimization.- Newton's Method for Equations and Inequalities.- Finite Minimax and Constrained Optimization.- Optimality Conditions for Minimax.- Optimality Conditions for Constrained Optimization.- Algorithm Models and Convergence Conditions II.- First-Order Minimax Algorithms.- Newton's Method for Minimax Problems.- Phase I. Phase II Methods of Centers .- Penalty Function Algorithms.- An Augmented Lagrangian Method.