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A descent approach to solving the complementary programming problem

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  • V. Venkateswaran

Abstract

In recent years, much attention has focused on mathematical programming problems with equilibrium constraints. In this article we consider the case where the constraints are complementarity constraints. Problems of this type arise, for instance, in the design of traffic networks. We develop here a descent algorithm for this problem that will converge to a local optimum in a finite number of iterations. The method involves solving a sequence of subproblems that are linear programs. Computational tests comparing our algorithm with the branch‐and‐bound algorithm in [7] bear out the efficacy of our method. When solving large problems, there is a definite advantage to coupling both methods. A local optimum incumbent provided by our algorithm can significantly reduce the computational effort required by the branch‐and‐bound algorithm.

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  • V. Venkateswaran, 1991. "A descent approach to solving the complementary programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 679-698, October.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:5:p:679-698
    DOI: 10.1002/1520-6750(199110)38:53.0.CO;2-S
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    1. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    2. Daniel Solow & Partha Sengupta, 1985. "A finite descent theory for linear programming, piecewise linear convex minimization, and the linear complementarity problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(3), pages 417-431, August.
    3. Paparrizos, Konstantinos & Solow, Daniel, 1989. "A finite improvement algorithm for the linear complementarity problem," European Journal of Operational Research, Elsevier, vol. 39(3), pages 305-324, April.
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