Set-Valued and Variational Analysis

, Volume 22, Issue 3, pp 557–573 | Cite as

A Proximal Point-Type Method for Multicriteria Optimization

  • G. C. Bento
  • J. X. Cruz Neto
  • A. Soubeyran


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.


Proximal Multicriteria optimization Quasi-convexity Fejér convergence Weak sharp 

Mathematics Subject Classifications (2010)

90C30 26B25 65K05 53C21 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.IME - Instituto de Matemática e EstatísticaUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.CCN, DM, Universidade Federal do PiauíTerezinaBrazil
  3. 3.Aix-Marseille School of EconomicsAix-Marseille University, CNRS EHESSMarseilleFrance

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