Using projected cutting planes in the extended cutting plane method

Abstract

In this paper we show that simple projections can improve the algorithmic performance of cutting plane-based optimization methods. Projected cutting planes can, for example, be used as alternatives to standard cutting planes or supporting hyperplanes in the extended cutting plane (ECP) method. In the paper we analyse the properties of such an algorithm and prove that it will converge to a global optimum for smooth and nonsmooth convex mixed integer nonlinear programming problems. Additionally, we show that we are able to solve two old but very difficult facility layout problems (FLP), with previously unknown optimal solutions, to verified global optimum by using projected cutting planes in the algorithm. These solution results are also given in the paper.