Mixed linear complementarity problem

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Mixed linear complementarity problem (MLCP) is a math optimization problem that extends the linear complementarity problem by allowing some variables to be free (not restricted to be nonnegative). You seek vectors that satisfy a set of linear equalities and inequalities together with complementarity conditions, where for some pairs at least one member must be zero. Some components must be nonnegative, while others can take any real value. MLCPs model situations with both constrained and free variables and are used in engineering, economics, and game theory. They can often be reformulated as standard LCPs or solved with specialized algorithms.