# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.01893