GLOBAL OPTIMIZATION PROBLEM WITH MULTIPLE REVERSE CONVEX CONSTRAINTS AND ITS APPLICATION TO OUT-OF-ROUNDNESS PROBLEM

Abstract

We consider a global minimization problem: min{c^Tx + d^Ty | x ∈ X, y ∈ Y ＼ ∪^<m_2>_<h=1> G_h, (x, y) ∈ F}, where X and Y are polytopes in R<n_1> and R<n_2>, respectively; F is a closed convex set in R<n_1+n_2>, and G_h (h = 1,…, m_2) is an open convex set in R<n_2>. We propose an alogorithm based on a combination of polyhedral outer approximation, branch-and-bound and cutting plane techniques. We also show that the out-of-roundness problem can be solved by the algorithm.