LCQPow -- A Solver for Linear Complementarity Quadratic Programs

TL;DR

This paper introduces LCQPow, an open-source C++ solver for quadratic programming problems with linear complementarity constraints, addressing their nonconvex and nonsmooth nature with an improved sequential convex programming approach.

Contribution

The paper presents LCQPow, a novel solver that extends existing algorithms with new features, demonstrating competitive performance on benchmark problems.

Findings

LCQPow effectively solves complex quadratic complementarity problems.

It outperforms some existing solvers in benchmark tests.

The solver is open-source and adaptable for various applications.

Abstract

In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in engineering and economics, and they are challenging to solve due to their structural violation of standard constraint qualifications, and highly nonconvex, nonsmooth feasible sets. This work extends a previously presented algorithm based on a sequential convex programming approach applied to a standard penalty reformulation. We examine the behavior of local convergence and introduce new algorithmic features. Competitive performance profiles are presented in comparison to state-of-the-art solvers and solution variants in both existing and new benchmarks.