GLOBAL OPTIMIZATION PROBLEM WITH MULTIPLE REVERSE CONVEX CONSTRAINTS AND ITS APPLICATION TO OUT-OF-ROUNDNESS PROBLEM
Yang Dai, Jianming Shi, Yoshitsugu Yamamoto · Journal of the Operations Research Society of Japan · 1996
We consider a global minimization problem: min{c^Tx + d^Ty | x ∈ X, y ∈ Y ＼ ∪^ _ G_h, (x, y) ∈ F}, where X and Y are polytopes in R and R , respectively; F is a closed convex set in R , and G_h (h = 1,…, m_2) is an open convex set in R . 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.