IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i1d10.1007_s10898-020-00969-x.html
   My bibliography  Save this article

Multi-objective convex polynomial optimization and semidefinite programming relaxations

Author

Listed:
  • Jae Hyoung Lee

    (Pukyong National University)

  • Nithirat Sisarat

    (Naresuan University)

  • Liguo Jiao

    (Soochow University)

Abstract

This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization problem $$({\mathrm{P}}_{z})$$ ( P z ) and does not destroy the properties of convexity, is considered. First, we show an existence result for efficient solutions to problem (MP) under some mild assumption. Then, for problem $$(P_{z})$$ ( P z ) , we establish two kinds of representations of non-negativity of convex polynomials over convex semi-algebraic sets, and propose two kinds of finite convergence results of the Lasserre-type hierarchy of semidefinite programming relaxations for problem $$({\mathrm{P}}_{z})$$ ( P z ) under suitable assumptions. Finally, we show that finding efficient solutions to problem (MP) can be achieved successfully by solving hierarchies of semidefinite programming relaxations and checking a flat truncation condition.

Suggested Citation

  • Jae Hyoung Lee & Nithirat Sisarat & Liguo Jiao, 2021. "Multi-objective convex polynomial optimization and semidefinite programming relaxations," Journal of Global Optimization, Springer, vol. 80(1), pages 117-138, May.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-020-00969-x
    DOI: 10.1007/s10898-020-00969-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00969-x
    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/s10898-020-00969-x?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. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    2. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Linear Programming Using MATLAB®," Springer Optimization and Its Applications, Springer, number 978-3-319-65919-0, June.
    3. Gorissen, B.L. & den Hertog, D., 2012. "Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization," Discussion Paper 2012-031, Tilburg University, Center for Economic Research.
    4. Gorissen, B.L. & den Hertog, D., 2012. "Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization," Other publications TiSEM 666c5307-4a4e-4be4-a0d0-b, Tilburg University, School of Economics and Management.
    5. Dinh The Luc, 2016. "Multiobjective Linear Programming," Springer Books, Springer, edition 1, number 978-3-319-21091-9, December.
    6. Nikolaos Ploskas & Nikolaos Samaras, 2017. "Correction to: Linear Programming Using MATLAB®," Springer Optimization and Its Applications, in: Linear Programming Using MATLAB®, pages E1-E3, Springer.
    7. Jae Hyoung Lee & Liguo Jiao, 2018. "Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 428-455, February.
    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. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    2. Feng Guo & Liguo Jiao, 2023. "A new scheme for approximating the weakly efficient solution set of vector rational optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 905-930, August.

    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. Feng Guo & Liguo Jiao, 2023. "A new scheme for approximating the weakly efficient solution set of vector rational optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 905-930, August.
    2. Dan A. Iancu & Nikolaos Trichakis, 2014. "Pareto Efficiency in Robust Optimization," Management Science, INFORMS, vol. 60(1), pages 130-147, January.
    3. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    4. Marianna E.-Nagy & Anita Varga, 2023. "A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 691-711, September.
    5. Sophia Voulgaropoulou & Nikolaos Samaras & Nikolaos Ploskas, 2022. "Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks," Mathematics, MDPI, vol. 10(7), pages 1-21, March.
    6. Mohand Bentobache & Mohamed Telli & Abdelkader Mokhtari, 2022. "New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 82(4), pages 659-689, April.
    7. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    8. Thai Doan Chuong, 2021. "Optimality and duality in nonsmooth composite vector optimization and applications," Annals of Operations Research, Springer, vol. 296(1), pages 755-777, January.
    9. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    10. Siming Pan & Shaokai Lu & Kaiwen Meng & Shengkun Zhu, 2021. "Trade-Off Ratio Functions for Linear and Piecewise Linear Multi-objective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 402-419, February.
    11. Xi Yin Zheng & Xiaoqi Yang, 2021. "Fully Piecewise Linear Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 461-490, August.
    12. Zhao, Meng & Wang, Yajun & Zhang, Xueyi & Xu, Chang, 2023. "Online doctor-patient dynamic stable matching model based on regret theory under incomplete information," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    13. Liguo Jiao & Jae Hyoung Lee, 2021. "Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data," Annals of Operations Research, Springer, vol. 296(1), pages 803-820, January.
    14. Nguyen Ngoc Luan & Jen-Chih Yao, 2019. "Generalized polyhedral convex optimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 789-811, November.
    15. N. Mahdavi-Amiri & F. Salehi Sadaghiani, 2017. "Strictly feasible solutions and strict complementarity in multiple objective linear optimization," 4OR, Springer, vol. 15(3), pages 303-326, September.
    16. Rogério A. Rocha & Paulo R. Oliveira & Ronaldo M. Gregório & Michael Souza, 2016. "A Proximal Point Algorithm with Quasi-distance in Multi-objective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 964-979, December.
    17. Feng Guo & Liguo Jiao, 2021. "On solving a class of fractional semi-infinite polynomial programming problems," Computational Optimization and Applications, Springer, vol. 80(2), pages 439-481, November.
    18. N. T. T. Huong & J.-C. Yao & N. D. Yen, 2020. "Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets," Journal of Global Optimization, Springer, vol. 78(3), pages 545-562, November.

    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:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-020-00969-x. 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.