Global optimization using interval analysis

Hansen E.

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”