A descent approach to solving the complementary programming problem

V. Venkateswaran

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)679-698
Number of pages20
JournalNaval Research Logistics Quarterly
Issue number5
StatePublished - Oct 1991
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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