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Proximal Point Algorithms for Multi-criteria Optimization with the Difference of Convex Objective Functions

Author

Listed:
  • Ying Ji

    (University of Shanghai for Science and Technology
    Harbin Institute of Technology
    National University of Singapore)

  • Mark Goh

    (National University of Singapore
    National University of Singapore)

  • Robert Souza

    (National University of Singapore)

Abstract

This paper focuses on solving a class of multi-criteria optimization with the difference of convex objective functions. Proximal point algorithms, extensively studied for scalar optimization, are extended to our setting. We show that the proposed algorithms are well posed and globally convergent to a critical point. For an application, the new methods are used to a multi-criteria model arising in portfolio optimization. The numerical results show the efficiency of our methods.

Suggested Citation

  • Ying Ji & Mark Goh & Robert Souza, 2016. "Proximal Point Algorithms for Multi-criteria Optimization with the Difference of Convex Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 280-289, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-015-0847-0
    DOI: 10.1007/s10957-015-0847-0
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    References listed on IDEAS

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    1. Hwang, Soosung & Satchell, Stephen E, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 4(4), pages 271-296, October.
    2. Glaydston Carvalho Bento & J.X. Cruz Neto & Antoine Soubeyran, 2014. "A Proximal Point-Type Method for Multicriteria Optimization," Post-Print hal-01463765, HAL.
    3. Villacorta, Kely D.V. & Oliveira, P. Roberto, 2011. "An interior proximal method in vector optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 485-492, November.
    4. Qu, Shaojian & Zhang, Kecun & Wang, Fusheng, 2008. "A global optimization using linear relaxation for generalized geometric programming," European Journal of Operational Research, Elsevier, vol. 190(2), pages 345-356, October.
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    Cited by:

    1. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    2. Outi Montonen & Kaisa Joki, 2018. "Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints," Journal of Global Optimization, Springer, vol. 72(3), pages 403-429, November.

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