[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v265y2018i1p39-48.html
   My bibliography  Save this article

On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization

Author

Listed:
  • Fakhar, Majid
  • Mahyarinia, Mohammad Reza
  • Zafarani, Jafar
Abstract
We introduce a new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions. In addition, we present a robust duality theory and Mond–Weir type duality for an uncertain multiobjective optimization problem. Furthermore, some nonsmooth saddle-point theorems are obtained under our generalized convexity assumption. Finally we show the viability of our new concept of generalized convexity for robust optimization and portfolio optimization.

Suggested Citation

  • Fakhar, Majid & Mahyarinia, Mohammad Reza & Zafarani, Jafar, 2018. "On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization," European Journal of Operational Research, Elsevier, vol. 265(1), pages 39-48.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:39-48
    DOI: 10.1016/j.ejor.2017.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717307154
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.08.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    2. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    3. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    4. Xidonas, Panos & Hassapis, Christis & Soulis, John & Samitas, Aristeidis, 2017. "Robust minimum variance portfolio optimization modelling under scenario uncertainty," Economic Modelling, Elsevier, vol. 64(C), pages 60-71.
    5. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    6. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    7. Bokrantz, Rasmus & Fredriksson, Albin, 2017. "Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 262(2), pages 682-692.
    8. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    9. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    10. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    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. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    2. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    3. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    4. Jie Wang & Shengjie Li & Min Feng, 2022. "Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 226-248, October.
    5. Xiangkai Sun & Kok Lay Teo & Liping Tang, 2019. "Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 984-1000, September.
    6. Fontem, Belleh & Smith, Jeremiah, 2019. "Analysis of a chance-constrained new product risk model with multiple customer classes," European Journal of Operational Research, Elsevier, vol. 272(3), pages 999-1016.
    7. Rekha R. Jaichander & Izhar Ahmad & Krishna Kummari & Suliman Al-Homidan, 2022. "Robust Nonsmooth Interval-Valued Optimization Problems Involving Uncertainty Constraints," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    8. Xiangkai Sun & Hongyong Fu & Jing Zeng, 2018. "Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    9. Zhu, Bo & Zhang, Tianlun, 2021. "Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    10. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    11. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.

    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. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    2. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "A Unified Characterization of Multiobjective Robustness via Separation," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 86-102, October.
    3. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    4. Jiang, Ling & Cao, Jinde & Xiong, Lianglin, 2019. "Generalized multiobjective robustness and relations to set-valued optimization," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 599-608.
    5. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    6. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    7. Schmidt, M. & Schöbel, Anita & Thom, Lisa, 2019. "Min-ordering and max-ordering scalarization methods for multi-objective robust optimization," European Journal of Operational Research, Elsevier, vol. 275(2), pages 446-459.
    8. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 466-493, February.
    9. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    10. Kaiqiang An & Guiyu Zhao & Jinjun Li & Jingsong Tian & Lihua Wang & Liang Xian & Chen Chen, 2023. "Best-Case Scenario Robust Portfolio: Evidence from China Stock Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 297-322, June.
    11. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
    12. Qamrul Hasan Ansari & Elisabeth Köbis & Pradeep Kumar Sharma, 2019. "Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 817-839, June.
    13. Yue Zhou-Kangas & Kaisa Miettinen, 2019. "Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 391-413, June.
    14. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    15. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    16. Bokrantz, Rasmus & Fredriksson, Albin, 2017. "Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 262(2), pages 682-692.
    17. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    18. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    19. Stefan Mišković, 2017. "A VNS-LP algorithm for the robust dynamic maximal covering location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1011-1033, October.
    20. Kang, Yan-li & Tian, Jing-Song & Chen, Chen & Zhao, Gui-Yu & Li, Yuan-fu & Wei, Yu, 2021. "Entropy based robust portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

    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:eee:ejores:v:265:y:2018:i:1:p:39-48. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.