A Proximal Point-Type Method for Multicriteria Optimization

Glaydston Carvalho Bento, J.X. Cruz Neto and Antoine Soubeyran

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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.

Keywords: Fejér convergence; Multicriteria optimization; Proximal; Quasi-convexity; Weak sharp (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

Published in Set-Valued and Variational Analysis, 2014, 22 (3), pp.557--573. ⟨10.1007/s11228-014-0279-2⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01463765

DOI: 10.1007/s11228-014-0279-2

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