Global Optimization Using Interval Analysis

by Hansen

This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. The latter can be unconstrained or have inequality and/or equality constraints. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.

This edition expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. It is shown that proof of existence and uniqueness of solutions can be obtained as a simple byproduct of computing a solution.

Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis, Second Edition simplifies algorithm construction and increases generality of interval arithmetic. Topics include

solving interval linear systems
the John conditions
Taylor series
slope expansions
quadratic equations and inequalities
new box splitting procedures
new "pillow" functions that replace peeling

Providing methods for solving perturbed systems of nonlinear equations and optimization problems—and including problems containing integers and nondifferentiable functions—this reference/text authoritatively informs nonlinear mathematical analysts, applied mathematicians, operations theorists, hardware and software engineers, programmers, and graduate-level students in these disciplines.

This book is printed on acid-free paper.

about the authors...

ELDON HANSEN is a consultant based in Los Altos, California, with over 40 years of experience in applied mathematics, computer science, physics, and engineering. He is the author or coauthor of three books and over 100 professional papers. Dr. Hansen received the A.B. (1950) and M.S. (1952) degrees in physics from the University of California, Berkeley, and the Ph.D. degree (1960) in mathematics from Stanford University, California.

G. WILLIAM WALSTER is a researcher with Sun Microsystems Laboratories, Mountain View, California, with over 40 years of experience in applied statistics, numerical analysis, and computing. He is the coauthor of two books and over 50 professional papers. Dr. Walster received the B.A. degree (1963) in psychology from Stanford University, California, and the Ph.D. degree (1968) in applied statistics from the Department of Educational Psychology at the University of Minnesota, Minneapolis.

256 pages, Hardcover

First published July 21, 1992