A comparison of solution approaches for the numerical treatment of or-constrained optimization problems

Abstract

Mathematical programs with or-constraints form a new class of disjunctive optimization problems with inherent practical relevance. In this paper, we provide a comparison of three different solution methods for the numerical treatment of this problem class which are inspired by classical approaches from disjunctive programming. First, we study the replacement of the or-constraints as nonlinear inequality constraints using suitable NCP-functions. Second, we transfer the or-constrained program into a mathematical program with switching or complementarity constraints which can be treated with the aid of well-known relaxation methods. Third, a direct Scholtes-type relaxation of the or-constraints is investigated. A numerical comparison of all these approaches which is based on three essentially different model programs from or-constrained optimization closes the paper.