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A Proximal Point-Type Method for Multicriteria Optimization

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Abstract

In this paper, we present a proximal point algorithm for multicriteria optimization, by assuming an iterative process which uses a variable scalarization function. With respect to the convergence analysis, firstly we show that, for any sequence generated from our algorithm, each accumulation point is a Pareto critical point for the multiobjective function. A more significant novelty here is that our paper gets full convergence for quasi-convex functions. In the convex or pseudo-convex cases, we prove convergence to a weak Pareto optimal point. Another contribution is to consider a variant of our algorithm, obtaining the iterative step through an unconstrained subproblem. Then, we show that any sequence generated by this new algorithm attains a Pareto optimal point after a finite number of iterations under the assumption that the weak Pareto optimal set is weak sharp for the multiobjective problem.

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Authors and Affiliations

  1. IME - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, GO, 74001-970, Caixa Postal: 131, Brazil

    G. C. Bento

  2. CCN, DM, Universidade Federal do Piauí, Terezina, PI, 64049-550, Brazil

    J. X. Cruz Neto

  3. Aix-Marseille School of Economics, Aix-Marseille University, CNRS EHESS, Marseille, France

    A. Soubeyran

Authors
  1. G. C. Bento
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  2. J. X. Cruz Neto
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  3. A. Soubeyran
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Correspondence to G. C. Bento.

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Bento, G.C., Cruz Neto, J.X. & Soubeyran, A. A Proximal Point-Type Method for Multicriteria Optimization. Set-Valued Var. Anal 22, 557–573 (2014). https://doi.org/10.1007/s11228-014-0279-2

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