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Coercivity and generalized proximal algorithms: application—traveling around the world

Author

Listed:
  • Erik Alex Papa Quiroz

    (UNMSM - Universidad Nacional Mayor de San Marcos, Universidad Privada del Norte, UFG - Universidade Federal de Goiás [Goiânia])

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Paulo Roberto Oliveira

    (PESC/COPPE-UFRJ - Programa de Engenharia de Sistemas e Computação - COPPE-UFRJ - Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia - UFRJ - Universidade Federal do Rio de Janeiro [Brasil] = Federal University of Rio de Janeiro [Brazil] = Université fédérale de Rio de Janeiro [Brésil])

Abstract

We present an inexact proximal point algorithm using quasi distances to solve a minimization problem in the Euclidean space. This algorithm is motivated by the proximal methods introduced by Attouch et al., section 4, (Math Program Ser A, 137: 91–129, 2013) and Solodov and Svaiter (Set Valued Anal 7:323–345, 1999). In contrast, in this paper we consider quasi distances, arbitrary (non necessary smooth) objective functions, scalar errors in each objective regularized approximation and vectorial errors on the residual of the regularized critical point, that is, we have an error on the optimality condition of the proximal subproblem at the new point. We obtain, under a coercivity assumption of the objective function, that all accumulation points of the sequence generated by the algorithm are critical points (minimizer points in the convex case) of the minimization problem. As an application we consider a human location problem: How to travel around the world and prepare the trip of a lifetime.

Suggested Citation

  • Erik Alex Papa Quiroz & Antoine Soubeyran & Paulo Roberto Oliveira, 2023. "Coercivity and generalized proximal algorithms: application—traveling around the world," Post-Print hal-03665851, HAL.
    • Handle: RePEc:hal:journl:hal-03665851
    DOI: 10.1007/s10479-022-04725-0
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03665851
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    References listed on IDEAS

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    1. Levin, V. L., 1991. "Some applications of set-valued mappings in mathematical economics," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 69-87.
    2. Truong Quang Bao & Antoine Soubeyran, 2019. "Variational principles in set optimization with domination structures and application to changing jobs," Post-Print hal-02497051, HAL.
    3. G. C. Bento & A. Soubeyran, 2015. "Generalized Inexact Proximal Algorithms: Routine’s Formation with Resistance to Change, Following Worthwhile Changes," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 172-187, July.
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    Cited by:

    1. Erik Papa Quiroz & Antoine Soubeyran, 2024. "Local proximal algorithms in Riemannian manifolds: Application to the behavioral traveler's problem," Post-Print hal-04930974, HAL.

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    More about this item

    Keywords

    Proximal point methods; Inexact algorithms; Coercivity; Quasi distances; Variational rationality; Traveler problem;
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