LCP theory refers to the **Linear Complementarity Problem** (LCP), a mathematical framework used primarily in optimization and mathematical programming. The LCP provides a way to describe and analyze systems that can be represented through inequalities and complementarity conditions. The LCP can be formally stated as follows: Given a matrix \( M \) and a vector \( q \), find vectors \( z \) and \( w \) such that: 1. \( z = Mx + q \) 2.
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