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

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Abstract

We establish the first rate of convergence result for the class of derivative-free descent methods for solving complementarity problems. The algorithm considered here is based on the implicit Lagrangian reformulation [26, 35] of the nonlinear complementarity problem, and makes 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 rate to the solution of the problem.

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Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI, 53706, U.S.A

    O.L. Mangasarian

  2. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, 22460-320, Brazil

    M.V. Solodov

Authors
  1. O.L. Mangasarian
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  2. M.V. Solodov
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Mangasarian, O., Solodov, M. A Linearly Convergent Derivative-Free Descent Method for Strongly Monotone Complementarity Problems. Computational Optimization and Applications 14, 5–16 (1999). https://doi.org/10.1023/A:1008752626695

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