Overview

This book presents an in-depth study and a solution technique for an important class of optimization problems. This class is characterized by special constraints: parameter-dependent convex programs, variational inequalities or complementarity problems. All these so-called equilibrium constraints are mostly treated in a convenient form of generalized equations. The book begins with a chapter on auxiliary results followed by a description of the main numerical tools: a bundle method of nonsmooth optimization and a nonsmooth variant of Newton's method. Following this, stability and sensitivity theory for generalized equations is presented, based on the concept of strong regularity. This enables one to apply the generalized differential calculus for Lipschitz maps to derive optimality conditions and to arrive at a solution method. A large part of the book focuses on applications coming from continuum mechanics and mathematical economy. A series of nonacademic problems is introduced and analyzed in detail. Each problem is accompanied with examples that show the efficiency of the solution method. This book is addressed to applied mathematicians and engineers working in continuum mechanics, operations research and economic modelling. Students interested in optimization will also find the book useful.

Full Product Details

Author:   Jiri Outrata ,  M. Kocvara ,  J. Zowe
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. Softcover of orig. ed. 1998
Volume:   28
Dimensions:   Width: 16.00cm , Height: 1.80cm , Length: 24.00cm
Weight:   0.513kg
ISBN:  

9781441948045

ISBN 10:   144194804
Pages:   274
Publication Date:   19 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

I Theory.- 1. Introduction.- 2. Auxiliary Results.- 3. Algorithms of Nonsmooth Optimization.- 4. Generalized Equations.- 5. Stability of Solutions to Perturbed Generalized Equations.- 6. Derivatives of Solutions to Perturbed Generalized Equations.- 7. Optimality Conditions and a Solution Method.- II Applications.- 8. Introduction.- 9. Membrane with Obstacle.- 10. Elasticity Problems with Internal Obstacles.- 11. Contact Problem with Coulomb Friction.- 12. Economic Applications.- Appendices.- A-Cookbook.- A.1 Problem.- A.2 Assumptions.- A.3 Formulas.- B-Basic facts on elliptic boundary value problems.- B.1 Distributions.- B.2 Sobolev spaces.- B.3 Elliptic problems.- C-Complementarity problems.- C.1 Proof of Theorem 4.7.- C.2 Supplement to proof of Theorem 4.9.- References.

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