Nonsmooth Equations In Optimization
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Nonsmooth Equations in Optimization
Author: Diethard Klatte
language: en
Publisher: Springer Science & Business Media
Release Date: 2002-05-31
The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular: an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings; a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions; an analysis of generalized Newton methods based on linear and nonlinear approximations; the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations; a rich collection of instructive examples and exercises.£/LIST£ Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers and advanced students who wish to get insights into problems, future directions and recent developments.
Nonsmooth Approach to Optimization Problems with Equilibrium Constraints
Author: Jiri Outrata
language: en
Publisher: Springer Science & Business Media
Release Date: 1998-07-31
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.
Nonsmooth Optimization
Author: Marko M. Mäkelä
language: en
Publisher: World Scientific Publishing Company Incorporated
Release Date: 1992-01-01
Introduces various methods for nonsmooth optimization and applies these methods to solve discretized nonsmooth optimal control problems of systems governed by boundary value problems. Annotation copyrighted by Book News, Inc., Portland, OR