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A Proximal Point-Type Method for Multicriteria Optimization

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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Submitted on : Thursday, February 9, 2017 - 4:40:05 PM
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Glaydston Carvalho Bento, J.X. Cruz Neto, Antoine Soubeyran. A Proximal Point-Type Method for Multicriteria Optimization. Set-Valued and Variational Analysis, Springer, 2014, 22 (3), pp.557--573. ⟨10.1007/s11228-014-0279-2⟩. ⟨hal-01463765⟩



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