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Nonlinear Programming and Variational Inequality Problems : A Unified Approach - Michael Patriksson

Nonlinear Programming and Variational Inequality Problems

A Unified Approach

Hardcover

Published: 30th November 1998
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Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi­ mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal­ ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Preface
Introduction
Technical Preliminaries
Instances of the Cost Approximation Algorithm
Merit Functions for Variational Inequality Problems
Convergence of the CA Algorithm for Nonlinear Programs
Convergence of the CA Algorithm for Variational Inequality Problems
Finite Identification of Active Constraints and of Solutions
Parallel and Sequential Decomposition CA Algorithms
A Column Generation/Simplicial Decomposition Algorithm
A. Definitions
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792354550
ISBN-10: 0792354559
Series: Applied Optimization
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 336
Published: 30th November 1998
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 3.18
Weight (kg): 1.49