A comparison of first-order methods for the numerical solution of or-constrained optimization problems

TL;DR

This paper compares three first-order methods for solving or-constrained optimization problems, focusing on their numerical performance and practical applicability.

Contribution

It provides a systematic numerical comparison of three approaches inspired by disjunctive programming for or-constrained problems.

Findings

Different methods show varying efficiency depending on problem structure

Relaxation techniques can effectively handle switching or complementarity constraints

Numerical results highlight strengths and limitations of each approach

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 first-order 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.