Technical Note—Complementary Programming

Toshihide Ibaraki
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Toshihide Ibaraki: Kyoto University, Kyoto, Japan

Operations Research, 1971, vol. 19, issue 6, 1523-1529

Abstract: A mathematical programming problem P : minimize z = d T x + e T u + f T v subject to Ax + Bu + Cv ≧ g , x , u , v ≧ 0, u T v = 0, is called a complementary programming ( CP ) problem. The condition u T v = 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.

Date: 1971
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