Technical Note—Complementary Programming

A mathematical programming problem P: minimize z = d_Tx + e_Tu + f_Tv subject to Ax + Bu + Cv ≧ g, x, u, v ≧ 0, u^Tv = 0, is called a complementary programming (CP) problem. The condition u^Tv = 0 distinguishes CP problems from ordinary LP problems. A variety of nonlinear programming problems can be formulated in this form, including absolute-value programming problems, 0-1 mixed-integer-programming problems, quadratic-programming problems, and so forth. This paper proposes a branch-and-bound algorithm for CP problems and reports some computational results.