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Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds

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Abstract

In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.

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Authors and Affiliations

  1. Universidad Nacional Mayor de San Marcos and Universidad Privada del Norte, Lima, Peru

    Erik Alex Papa Quiroz

  2. Universidade Federal do Rio de Janeiro and Centro de Tecnologia Mineral-CETEM, Rio de Janeiro, Brazil

    Nancy Baygorrea Cusihuallpa

  3. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Nelson Maculan

Authors
  1. Erik Alex Papa Quiroz
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  2. Nancy Baygorrea Cusihuallpa
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  3. Nelson Maculan
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Correspondence to Erik Alex Papa Quiroz.

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Communicated by Alexandru Kristály.

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Papa Quiroz, E.A., Baygorrea Cusihuallpa, N. & Maculan, N. Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds. J Optim Theory Appl 186, 879–898 (2020). https://doi.org/10.1007/s10957-020-01725-7

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  • DOI: https://doi.org/10.1007/s10957-020-01725-7

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