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Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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