Rigorous Global Search: Continuous Problems / Edition 1

by R. Baker Kearfott

Overview

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.

Product Details

ISBN-13:	9780792342380
Publisher:	Springer US
Publication date:	10/31/1996
Series:	Nonconvex Optimization and Its Applications , #13
Edition description:	1996
Pages:	264
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1 Preliminaries.- 2 Software Environments.- 3 On Preconditioning.- 4 Verified Solution of Nonlinear Systems.- 5 Optimization.- 6 Non-Differentiable Problems.- 7 Use of Intermediate Quantities in THE Expression Values.- References.

Editorial Reviews

A self-contained introduction to the underlying techniques and theory of the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. After introductory and survey material, chapters offer unique research results and nontraditional ideas concerning nonsmooth optimization. Includes chapter examples and exercises. Can be used as a graduate text or reference on interval arithmetic, automatic differentiation, and interval fixed point theory, as well as numerical analysis, optimization, and operations research. Can also be used as guide to the software for both the interval arithmetic package and the automatic differentiation package. Annotation c. by Book News, Inc., Portland, Or.

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