IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v316y2022i2d10.1007_s10479-021-04052-w.html
   My bibliography  Save this article

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

Author

Listed:
  • G. C. Bento

    (Universidade Federal de Goiás)

  • J. X. Cruz Neto

    (Universidade Federal do Piauí)

  • P. A. Soares

    (Universidade Etadual do Piauí)

  • A. Soubeyran

    (Aix-Marseille University (Aix-Marseille School of Economics))

Abstract

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

Suggested Citation

  • G. C. Bento & J. X. Cruz Neto & P. A. Soares & A. Soubeyran, 2022. "A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires," Annals of Operations Research, Springer, vol. 316(2), pages 1301-1318, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-021-04052-w
    DOI: 10.1007/s10479-021-04052-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-021-04052-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-021-04052-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. J. X. Cruz Neto & P. R. Oliveira & P. A. Soares & A. Soubeyran, 2014. "Proximal Point Method on Finslerian Manifolds and the “Effort–Accuracy” Trade-off," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 873-891, September.
    2. J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    3. Vladimir Bulavsky & Vyacheslav Kalashnikov, 1998. "A Newton-like approach to solvingan equilibrium problem," Annals of Operations Research, Springer, vol. 81(0), pages 115-128, June.
    4. Gayatri Pany & Ram N. Mohapatra & Sabyasachi Pani, 2018. "Solution of a class of equilibrium problems and variational inequalities in FC spaces," Annals of Operations Research, Springer, vol. 269(1), pages 565-582, October.
    5. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    6. Glaydston C. Bento & Jefferson G. Melo, 2012. "Subgradient Method for Convex Feasibility on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 773-785, March.
    7. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, January.
    8. Xiaomin Zhang & Zezhong Wu, 2013. "Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems," Advances in Operations Research, Hindawi, vol. 2013, pages 1-9, November.
    9. Edvaldo E. A. Batista & Glaydston de Carvalho Bento & Orizon P. Ferreira, 2016. "Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 916-931, September.
    10. Jianke Zhang, 2013. "Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, December.
    11. E. Papa Quiroz, 2013. "An extension of the proximal point algorithm with Bregman distances on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 56(1), pages 43-59, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Glaydston C. Bento & João X. Cruz Neto & Jurandir O. Lopes & Ítalo D. L. Melo & Pedro Silva Filho, 2024. "A New Approach About Equilibrium Problems via Busemann Functions," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 428-436, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. João Carlos de O. Souza, 2018. "Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 745-760, December.
    2. J. X. Cruz Neto & F. M. O. Jacinto & P. A. Soares & J. C. O. Souza, 2018. "On maximal monotonicity of bifunctions on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 72(3), pages 591-601, November.
    3. G. C. Bento & J. X. Cruz Neto, 2013. "A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 125-137, October.
    4. Xiao-bo Li & Li-wen Zhou & Nan-jing Huang, 2016. "Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 830-849, March.
    5. Glaydston Carvalho Bento & João Xavier Cruz Neto & Paulo Roberto Oliveira, 2016. "A New Approach to the Proximal Point Method: Convergence on General Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 743-755, March.
    6. Xiangmei Wang & Chong Li & Jen-Chih Yao, 2016. "On Some Basic Results Related to Affine Functions on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 783-803, September.
    7. Oliver Stein & Nathan Sudermann-Merx, 2016. "The Cone Condition and Nonsmoothness in Linear Generalized Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 687-709, August.
    8. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    9. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    10. Balendu Bhooshan Upadhyay & Arnav Ghosh, 2023. "On Constraint Qualifications for Mathematical Programming Problems with Vanishing Constraints on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 1-35, October.
    11. Alexey Izmailov & Mikhail Solodov, 2014. "On error bounds and Newton-type methods for generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 201-218, October.
    12. J. H. Wang & G. López & V. Martín-Márquez & C. Li, 2010. "Monotone and Accretive Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 691-708, September.
    13. J. H. Wang, 2011. "Convergence of Newton’s Method for Sections on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 125-145, January.
    14. Migot, Tangi & Cojocaru, Monica-G., 2020. "A parametrized variational inequality approach to track the solution set of a generalized nash equilibrium problem," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1136-1147.
    15. Denizalp Goktas & Jiayi Zhao & Amy Greenwald, 2023. "T\^atonnement in Homothetic Fisher Markets," Papers 2306.04890, arXiv.org.
    16. Amir Gandomi & Amirhossein Bazargan & Saeed Zolfaghari, 2019. "Designing competitive loyalty programs: a stochastic game-theoretic model to guide the choice of reward structure," Annals of Operations Research, Springer, vol. 280(1), pages 267-298, September.
    17. Vladimir Shikhman, 2022. "On local uniqueness of normalized Nash equilibria," Papers 2205.13878, arXiv.org.
    18. Ming Hu & Masao Fukushima, 2011. "Variational Inequality Formulation of a Class of Multi-Leader-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 455-473, December.
    19. Victor Picheny & Mickael Binois & Abderrahmane Habbal, 2019. "A Bayesian optimization approach to find Nash equilibria," Journal of Global Optimization, Springer, vol. 73(1), pages 171-192, January.
    20. X. M. Wang & J. H. Wang & C. Li, 2023. "Convergence of Inexact Steepest Descent Algorithm for Multiobjective Optimizations on Riemannian Manifolds Without Curvature Constraints," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 187-214, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-021-04052-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.