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Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds

Author

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  • Erik Alex Papa Quiroz

    (Universidad Nacional Mayor de San Marcos and Universidad Privada del Norte)

  • Nancy Baygorrea Cusihuallpa

    (Universidade Federal do Rio de Janeiro and Centro de Tecnologia Mineral-CETEM)

  • Nelson Maculan

    (Universidade Federal do Rio de Janeiro)

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.

Suggested Citation

  • Erik Alex Papa Quiroz & Nancy Baygorrea Cusihuallpa & Nelson Maculan, 2020. "Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 879-898, September.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01725-7
    DOI: 10.1007/s10957-020-01725-7
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    References listed on IDEAS

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    Cited by:

    1. Xiaopeng Zhao & Jen-Chih Yao, 2022. "Linear convergence of a nonmonotone projected gradient method for multiobjective optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 577-594, March.
    2. G. C. Bento & J. X. Cruz Neto & L. V. Meireles & A. Soubeyran, 2022. "Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm," Annals of Operations Research, Springer, vol. 316(2), pages 1425-1443, September.
    3. Xiaopeng Zhao & Markus A. Köbis & Yonghong Yao & Jen-Chih Yao, 2021. "A Projected Subgradient Method for Nondifferentiable Quasiconvex Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 82-107, July.

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