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Logarithmic quasi-distance proximal point scalarization method for multi-objective programming

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  • Rocha, Rogério Azevedo
  • Oliveira, Paulo Roberto
  • Gregório, Ronaldo Malheiros
  • Souza, Michael

Abstract

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance. By restricting it to a certain class of quasi-distances that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence {(xk,zk)}⊂Rn×R++m generated by the method satisfies: {zk} is convergent; and {xk} is bounded and its accumulation points are weak Pareto solutions of the unconstrained multi-objective optimization problem

Suggested Citation

  • Rocha, Rogério Azevedo & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros & Souza, Michael, 2016. "Logarithmic quasi-distance proximal point scalarization method for multi-objective programming," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 856-867.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:856-867
    DOI: 10.1016/j.amc.2015.10.065
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    References listed on IDEAS

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    Cited by:

    1. Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    2. Rogério A. Rocha & Paulo R. Oliveira & Ronaldo M. Gregório & Michael Souza, 2016. "A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 964-979, December.

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