Introduction

Mathematical programs with complementarity constraints (MPCC) are optimization problems of the form

\[ \begin{aligned} \min \quad &\varphi := f(x, y, z) \\ \text{s.t.} \quad &h(x, y, z) = 0 \\ &g(x, y, z) \ge 0 \\ &0 \le x \perp y \ge 0 \end{aligned} \]

in which the last constraint means that either $x \in \mathbb{R}^n \ge 0$ or $y \in \mathbb{R}^n \ge 0$. They can be used to model processes that, for example, present switches or nonsmooth decisions with the advantage of incorporating discrete decisions in a single nonlinear programming (NLP) formulation^[1].

This library is intended to be a compilation of MPCC (Mathematical Programs with Complementarity Constraints) problems to test algorithms developed in Julia using JuMP as modeling language and to be used as case studies. It also contains an implementation of the first algorithm proposed by Leyffer et al (2006)^[2] that can be used to solve examples in this library.

Flash Tank Problem

Thermal Energy Storage Problem

Bioprocess Optimization Problem

1Lorenz T. Biegler. Nonlinear programming: concepts, algorithms, and applications to chemical processes. Vol. 10. Siam, 2010
2 Leyffer, S., López-Calva, G. and Nocedal, J. Interior methods for mathematical programs with complementarity constraints. SIAM Journal on Optimization, 17(1), pp.52-77, 2006.