IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v185y2020i1d10.1007_s10957-020-01646-5.html
   My bibliography  Save this article

Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints

Author

Listed:
  • Thai Doan Chuong

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

We show that a separable polynomial program involving a box constraint enjoys a dual problem, that can be displayed in terms of sums of squares univariate polynomials. Under convexification and qualification conditions, we prove that a strong duality relation between the underlying separable polynomial problem and its corresponding dual holds, where the dual problem can be reformulated and solved as a semidefinite programming problem.

Suggested Citation

  • Thai Doan Chuong, 2020. "Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 289-299, April.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01646-5
    DOI: 10.1007/s10957-020-01646-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01646-5
    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/s10957-020-01646-5?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. H. Tuy & H. Tuan, 2013. "Generalized S-Lemma and strong duality in nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1045-1072, July.
    2. M. Ç. Pinar, 2004. "Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 433-440, August.
    3. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    4. Vaithilingam Jeyakumar & Zhiyou Wu, 2007. "Conditions For Global Optimality Of Quadratic Minimization Problems With Lmi Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 149-160.
    5. Chieu, N.H. & Jeyakumar, V. & Li, G., 2020. "Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality," European Journal of Operational Research, Elsevier, vol. 280(2), pages 441-452.
    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. Cao Thanh Tinh & Thai Doan Chuong, 2022. "Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 570-596, 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. Xue-Gang Zhou & Xiao-Peng Yang & Bing-Yuan Cao, 2015. "Global optimality conditions for cubic minimization problems with cubic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 243-264, December.
    2. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    3. X. Zheng & X. Sun & D. Li & Y. Xu, 2012. "On zero duality gap in nonconvex quadratic programming problems," Journal of Global Optimization, Springer, vol. 52(2), pages 229-242, February.
    4. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    5. Guoyin Li, 2012. "Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 710-726, March.
    6. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    7. Wu, Zhiyou & Tian, Jing & Quan, Jing & Ugon, Julien, 2014. "Optimality conditions and optimization methods for quartic polynomial optimization," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 968-982.
    8. Wu, Zhiyou & Tian, Jing & Ugon, Julien & Zhang, Liang, 2015. "Global optimality conditions and optimization methods for constrained polynomial programming problems," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 312-325.
    9. Z. Wu & J. Tian & J. Ugon, 2015. "Global optimality conditions and optimization methods for polynomial programming problems," Journal of Global Optimization, Springer, vol. 62(4), pages 617-641, August.
    10. Harish Palanthandalam-Madapusi & Tobin Van Pelt & Dennis Bernstein, 2009. "Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint," Computational Optimization and Applications, Springer, vol. 45(4), pages 533-549, December.
    11. Huu-Quang Nguyen & Ruey-Lin Sheu, 2019. "Geometric properties for level sets of quadratic functions," Journal of Global Optimization, Springer, vol. 73(2), pages 349-369, February.
    12. Z. Wu & G. Li & J. Quan, 2011. "Global optimality conditions and optimization methods for quadratic integer programming problems," Journal of Global Optimization, Springer, vol. 51(3), pages 549-568, November.
    13. Z. Y. Wu & Y. J. Yang & F. S. Bai & M. Mammadov, 2011. "Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 241-259, November.
    14. Wei Chen & Liansheng Zhang, 2010. "Global optimality conditions for quadratic 0-1 optimization problems," Journal of Global Optimization, Springer, vol. 46(2), pages 191-206, February.
    15. T. D. Chuong & V. Jeyakumar, 2018. "Generalized Lagrangian duality for nonconvex polynomial programs with polynomial multipliers," Journal of Global Optimization, Springer, vol. 72(4), pages 655-678, December.
    16. V. Jeyakumar & Guoyin Li, 2011. "Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems," Journal of Global Optimization, Springer, vol. 49(1), pages 1-14, January.
    17. Hossein Mohebi & Alexander Rubinov, 2006. "Metric Projection onto a Closed Set: Necessary and Sufficient Conditions for the Global Minimum," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 124-132, February.
    18. Amar Andjouh & Mohand Ouamer Bibi, 2022. "Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 360-378, January.
    19. V. Jeyakumar & G. Li, 2013. "Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty," Journal of Global Optimization, Springer, vol. 55(2), pages 209-226, February.
    20. Z. Y. Wu & V. Jeyakumar & A. M. Rubinov, 2007. "Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 123-130, April.

    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:185:y:2020:i:1:d:10.1007_s10957-020-01646-5. 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.