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A proximal method with logarithmic barrier for nonlinear complementarity problems

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Abstract

We study the proximal method with the regularized logarithmic barrier, originally stated by Attouch and Teboulle for positively constrained optimization problems, in the more general context of nonlinear complementarity problems with monotone operators. We consider two sequences generated by the method. We prove that one of them, called the ergodic sequence, is globally convergent to the solution set of the problem, assuming just monotonicity of the operator and existence of solutions; for convergence of the other one, called the proximal sequence, we demand some stronger property, like paramonotonicity of the operator or the so called “cut property” of the problem.

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Authors and Affiliations

  1. Instituto de Economia da, Universidade Federal de Rio de Janeiro, Avenida Pasteur 250, Rio de Janeiro, RJ, Brazil

    Rolando Gárciga Otero

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

    Alfredo Iusem

Authors
  1. Rolando Gárciga Otero
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  2. Alfredo Iusem
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Correspondence to Rolando Gárciga Otero.

Additional information

The work of this author was partially supported by PRONEX-Optimization. Partially supported by CNPq Grant No. 301280/86.

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Gárciga Otero, R., Iusem, A. A proximal method with logarithmic barrier for nonlinear complementarity problems. J Glob Optim 64, 663–678 (2016). https://doi.org/10.1007/s10898-015-0266-7

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  • DOI: https://doi.org/10.1007/s10898-015-0266-7

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