Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

TL;DR

This paper introduces a sequential linearization algorithm for bound-constrained mathematical programs with complementarity constraints, emphasizing active set estimation, descent enforcement, and convergence analysis, supported by preliminary numerical results.

Contribution

It presents a novel iterative method that solves linear programs with complementarity constraints to efficiently handle bound-constrained problems with complementarity conditions.

Findings

Algorithm converges to B-stationary points.

Preliminary numerical results show promising performance.

Fixing active constraints can accelerate convergence.

Abstract

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.