Linear programming with linear complementarity constraints (LPLCC) is an area of active research in Optimization, due to its many applications, algorithms, and theoretical existence results. In this paper, a number of formulations for important nonconvex optimization problems are first reviewed. The most relevant algorithms for computing a complementary feasible solution, a stationary point, and a global minimum for the LPLCC are also surveyed, together with some comments about their efficiency and efficacy in practice.
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