Reformulation of mathematical programming problems as linear complementarity problems and investigation of their solution methods

A family of complementarity problems is defined as extensions of the well-known linear complementarity problem (LCP). These are:

(i)	second linear complementarity problem (SLCP), which is an LCP extended by introducing further equality restrictions and unrestricted variables;
(ii)	minimum linear complementarity problem (MLCP), which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized;
(iii)	second minimum linear complementarity problem (SMLCP), which is an MLCP, but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value.

A number of well-known mathematical programming problems [namely, quadratic programming (convex, nonconvex, pseudoconvex, nonconvex), linear variational inequalities, bilinear programming, game theory, zero-one integer programming, fixed-charge problem, absolute value programming, variable separable programming] are reformulated as members of this family of four complementarity problems. A brief discussion of the main algorithms for these four problems is presented, together with some computational experience.