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We study relaxations for linear programs with complementarity constraints,especially instances whose complementary pairs of variables are notindependent. Our formulation is based on identifying vertex covers of theconflict graph of the instance and generalizes the extendedreformulation-linearization technique of Nguyen, Richard, and Tawarmalani toinstances with general complementarity conditions between variables. Wedemonstrate how to obtain strong cutting planes for our formulation from boththe stable set polytope and the boolean quadric polytope associated with acomplete bipartite graph. Through an extensive computational study for threetypes of practical problems, we assess the performance of our proposed linearrelaxation and new cutting-planes in terms of the optimality gap closed.

Relaxations and Cutting Planes for Linear Programs with Complementarity Constraints