A Linearly Convergent Derivative-Free Descent Method for Strongly Monotone Complementarity Problems

  • Authors:

  • O. L. Mangasarian;M. V. Solodov

  • Affiliations:

  • Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI 53706, U.S.A. olvi@cs.wisc.edu;Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil. solodov@impa.br

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 1999

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Abstract

We establish the first rate of convergence result for the class ofderivative-free descent methods for solving complementarity problems.The algorithm considered here isbased on the implicit Lagrangian reformulation[26, 35] of the nonlinear complementarity problem, andmakes use of the descent direction proposed in[42], but employs a different Armijo-type linesearch rule.We show that in the strongly monotone case,the iterates generated by the method converge globally at a linear rateto the solution of the problem.