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1 Prace Naukowe Politechniki Warszawskiej. Elektronika

1 2002

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Unconstrained and constrained global optimization using interval analysis

Kubica B., Niewiadomska-Szynkiewicz E.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2002

z. 139

185--199

This chapter presents techniques adressed to continuous, unconstrained and constrained optimization problems. Global optimization is defined as the problem of finding points on a bounded subset of X of Rn in which some real valued function f reaches its optimal (minimum or maximum) value. The algorithms considered are based on the branch-and-bound principles where the problem domain is partitioned iteratively. They apply interval arithmetic tools. The main objective is to discuss the advantages and disadvantages of existing algorithms and to provide some modifications for increasing their efficiency. The numerical results for several test problems are presented in the final part of the chapter.