Computational aspects on the use of cutting planes in global optimization

Minimization of a nonconvex objective function subject to linear inequality constraints can involve many local minima. Cutting plane methods for solving such problems have been proposed in the literature. This paper reports computational experience indicating that cutting methods do poorly on problems with dimension as low as ten. A geometric analysis of the conditions involved in cutting a polyhedron shows that: 1)The effect of a fixed depth cut decreases rapidly as dimension is increased, and 2)The approximation of a polyhedron by the cone formed by faces coincident to a given extreme point, becomes rapidly worse as dimension is increased.