IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v160y2014i3d10.1007_s10957-013-0392-7.html
   My bibliography  Save this article

A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes

Author

Listed:
  • Kely D. V. Villacorta

    (Federal University of Paraíba)

  • Paulo R. Oliveira

    (Federal University of Rio de Janeiro
    Cidade Universitária)

  • Antoine Soubeyran

    (CNRS & EHESS, Chateau Lafarge)

Abstract

Multiobjective optimization has a significant number of real-life applications. For this reason, in this paper we consider the problem of finding Pareto critical points for unconstrained multiobjective problems and present a trust-region method to solve it. Under certain assumptions, which are derived in a very natural way from assumptions used to establish convergence results of the scalar trust-region method, we prove that our trust-region method generates a sequence which converges in the Pareto critical way. This means that our generalized marginal function, which generalizes the norm of the gradient for the multiobjective case, converges to zero. In the last section of this paper, we give an application to satisficing processes in Behavioral Sciences. Multiobjective trust-region methods appear to be remarkable specimens of much more abstract satisficing processes, based on “variational rationality” concepts. One of their important merits is to allow for efficient computations. This is a striking result in Behavioral Sciences.

Suggested Citation

  • Kely D. V. Villacorta & Paulo R. Oliveira & Antoine Soubeyran, 2014. "A Trust-Region Method for Unconstrained Multiobjective Problems with Applications in Satisficing Processes," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 865-889, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0392-7
    DOI: 10.1007/s10957-013-0392-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0392-7
    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/s10957-013-0392-7?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. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    3. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
    4. Fabián Flores-Bazán & Dinh The Luc & Antoine Soubeyran, 2012. "Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 883-901, December.
    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 Carvalho Bento & Gemayqzel Bouza Allende & Yuri Rafael Leite Pereira, 2018. "A Newton-Like Method for Variable Order Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(1), pages 201-221, April.
    2. Morovati, Vahid & Pourkarimi, Latif, 2019. "Extension of Zoutendijk method for solving constrained multiobjective optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 44-57.
    3. Ana Luísa Custódio & Youssef Diouane & Rohollah Garmanjani & Elisa Riccietti, 2021. "Worst-Case Complexity Bounds of Directional Direct-Search Methods for Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 73-93, January.
    4. N. Eslami & B. Najafi & S. M. Vaezpour, 2023. "A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 212-239, January.
    5. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    6. Suyun Liu & Luis Nunes Vicente, 2023. "Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 165-186, July.

    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. 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.
    2. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    3. Antoine Soubeyran, 2023. "Variational rationality: Finding the inequations of motion of a person seeking to meet his needs," AMSE Working Papers 2309, Aix-Marseille School of Economics, France.
    4. Bento, G.C. & Cruz Neto, J.X. & Oliveira, P.R. & Soubeyran, A., 2014. "The self regulation problem as an inexact steepest descent method for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 235(3), pages 494-502.
    5. Antoine Soubeyran, 2022. "Variational rationality: Finding the inequations of motion of a person seeking to meet his needs," Working Papers hal-04065103, HAL.
    6. 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.
    7. Torgler, Benno & Schneider, Friedrich & Schaltegger, Christoph A., 2007. "With or Against the People? The Impact of a Bottom-Up Approach on Tax Morale and the Shadow Economy," Berkeley Olin Program in Law & Economics, Working Paper Series qt6331x6vz, Berkeley Olin Program in Law & Economics.
    8. Daniel Fonseca Costa & Francisval Carvalho & Bruno César Moreira & José Willer Prado, 2017. "Bibliometric analysis on the association between behavioral finance and decision making with cognitive biases such as overconfidence, anchoring effect and confirmation bias," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1775-1799, June.
    9. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    10. Jae Wook Yoo & Richard Reed & Shung Jae Shin & David J. Lemak, 2009. "Strategic Choice and Performance in Late Movers: Influence of the Top Management Team's External Ties," Journal of Management Studies, Wiley Blackwell, vol. 46(2), pages 308-335, March.
    11. Kazemi, Abolghasem & Moreno, Jovita & Iribarren, Diego, 2023. "Economic optimization and comparative environmental assessment of natural gas combined cycle power plants with CO2 capture," Energy, Elsevier, vol. 277(C).
    12. Giovanni Calice & Levent Kutlu & Ming Zeng, 2021. "Understanding US firm efficiency and its asset pricing implications," Empirical Economics, Springer, vol. 60(2), pages 803-827, February.
    13. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    14. José Castro Caldas & Helder Coelho, 1999. "The Origin of Institutions: Socio-Economic Processes, Choice, Norms and Conventions," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 2(2), pages 1-1.
    15. Nagler Matthew G., 2007. "Understanding the Internet's Relevance to Media Ownership Policy: A Model of Too Many Choices," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 7(1), pages 1-28, June.
    16. Ranganathan, Kavitha & Lejarraga, Tomás, 2021. "Elicitation of risk preferences through satisficing," Journal of Behavioral and Experimental Finance, Elsevier, vol. 32(C).
    17. Westerhoff Frank H., 2008. "The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 228(2-3), pages 195-227, April.
    18. Andrew Caplin & Mark Dean & Daniel Martin, 2011. "Search and Satisficing," American Economic Review, American Economic Association, vol. 101(7), pages 2899-2922, December.
    19. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    20. Lawrence Bunnell & Kweku-Muata Osei-Bryson & Victoria Y. Yoon, 0. "RecSys Issues Ontology: A Knowledge Classification of Issues for Recommender Systems Researchers," Information Systems Frontiers, Springer, vol. 0, pages 1-42.

    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:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0392-7. 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.