Introduction
The linear complementarity problem (LCP) can be stated as [1]:
| LCP Problem |
|---|
| \[\begin{align} &\text{Find $\color{darkred}x\ge 0,\color{darkred}w\ge 0$ such that:}\\ & \color{darkred}x^T\color{darkred}w = 0 \\ &\color{darkred}w =\color{darkblue}M \color{darkred}x + \color{darkblue}q\end{align}\] |
In many cases we require that \(\color{darkblue}M\) is positive definite.
The LCP has different applications, including in finance, physics, and economics [2]. Off-the-shelf LCP solvers are not widely available. Here I will show how to solve LCPs with other solvers. This question comes up now and then, so here is a short recipe post.
