Enumerative techniques for solving some nonconvex global optimization problems

Abstract

We give an overview on different methods for solving nonconvex minimization problems using techniques of enumeration of extreme points. The problems considered include concave, indefinite quadratic, and special structured problems such as the concave cost network flow problem and linear complementarity. For methods that enumerate the extreme points according to the ascending order of the value of a linear underestimating function we propose new techniques for obtaining such underestimators.