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A logarithmic-quadratic proximal point scalarization method for multiobjective programming

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Abstract

We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R n  to  R m with respect to the lexicographic order on R m and we add a variant of the logarithmic-quadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced in the quadratic term. The nonegative variables employed in the scalarization are placed in the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak pareto solution of the multiobjective optimization problem.

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Authors and Affiliations

  1. Technology and Languages Departament, Federal Rural University of Rio de Janeiro, Rua Capitão Chaves, N.0 60, Centro, Nova Iguaçu, Rio de Janeiro, CEP 26221-010, Brazil

    Ronaldo Gregório

  2. Computing and Systems Engineering Department, Federal University of Rio de Janeiro, Caixa Postal 68511, Rio de Janeiro, CEP 21945-970, Brazil

    Paulo Roberto Oliveira

Authors
  1. Ronaldo Gregório
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  2. Paulo Roberto Oliveira
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Correspondence to Ronaldo Gregório.

Additional information

This research was developed at the Computing and Systems Engineering Department of the Federal University of Rio de Janeiro and supported by CAPES while the first author was doctoral student.

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Gregório, R., Oliveira, P.R. A logarithmic-quadratic proximal point scalarization method for multiobjective programming. J Glob Optim 49, 281–291 (2011). https://doi.org/10.1007/s10898-010-9544-6

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  • DOI: https://doi.org/10.1007/s10898-010-9544-6

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