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Enumeration approach for linear complementarity problems based on a reformulation-linearization technique. (English) Zbl 0911.90328
Summary: We consider the linear complementarity problem (LCP) and present a global optimization algorithm based on an application of the reformulation linearization technique (RLT). The matrix $$M$$ associated with the LCP is not assumed to possess any special structure. In this approach, the LCP is formulated first as a mixed-integer 0-1 bilinear programming problem. The RLT scheme is then used to derive a new equivalent mixed-integer linear programming formulation of the LCP. An implicit enumeration scheme is developed that uses Lagrangian relaxation, strongest surrogate and strengthened cutting planes, and a heuristic, designed to exploit the strength of the resulting linearization. Computational experience on various test problems is presented.

##### MSC:
 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 90C11 Mixed integer programming
XMP
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##### References:
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