Tighter underestimator for bivariate global optimization

Abstract

We propose in this paper a tighter underestimator for \(C^{2}\)-nonconvex bivariate functions. We show that it is tighter than the classical \(\alpha -\)BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.