Linear complementarity problem

The Linear Complementarity Problem (LCP) is a mathematical problem that involves finding vectors that satisfy certain linear inequalities and equations. Specifically, the LCP can be formally defined as follows: Given a matrix \( M \) and a vector \( q \), the goal is to find a vector \( z \) such that: 1. \( z \geq 0 \) (the vector \( z \) is element-wise non-negative), 2.