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Finite convergence of algorithms for nonlinear programs and variational inequalities

  • F. Al-Khayyal
  • J. Kyparisis
Contributed Papers

Abstract

Algorithms for nonlinear programming and variational inequality problems are, in general, only guaranteed to converge in the limit to a Karush-Kuhn-Tucker point, in the case of nonlinear programs, or to a solution in the case of variational inequalities. In this paper, we derive sufficient conditions for nonlinear programs with convex feasible sets such that any convergent algorithm can be modified, by adding a convex subproblem with a linear objective function, to guarantee finite convergence in a generalized sense. When the feasible set is polyhedral, the subproblem is a linear program and finite convergence is obtained. Similar results are also developed for variational inequalities.

Key Words

Convergence of algorithms nonlinear programming variational inequalities 

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • F. Al-Khayyal
    • 1
  • J. Kyparisis
    • 2
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Department of Decision Sciences and Information Systems, College of Business AdministrationFlorida International UniversityMiami

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