23rd European Symposium on Computer Aided Process Engineering

comparison of two convex underestimation methods for quadratic functions

Anders Skjäl and Tapio Westerlund^∗,    Center of Excellence in Optimization and Systems Engineering, Åbo Akademi University, Biskopsgatan 8, 20500 Åbo, Finland, ^∗[e-mail]

Abstract

In this paper we compare two recently described methods for convex underestimation. The first method is a variant of the nondiagonal αBB methods studied by the authors. The second method depends on algebraic characterizations of positive polynomials. Positive polynomials on a compact semi-algebraic set can be decomposed as polynomial terms containing squares and the defining polynomials of the set. This characterization can be used for describing both the underestimation ...