Technical Note—Complementary Programming
- 1 October 1971
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research
- Vol. 19 (6) , 1523-1529
- https://doi.org/10.1287/opre.19.6.1523
Abstract
A mathematical programming problem P: minimize z = dTx + eTu + fTv subject to Ax + Bu + Cv ≧ g, x, u, v ≧ 0, uTv = 0, is called a complementary programming (CP) problem. The condition uTv = 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.Keywords
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