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On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems

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  • Xiangkai Sun

    (Chongqing Technology and Business University)

  • Jiayi Huang

    (Chongqing Technology and Business University)

  • Kok Lay Teo

    (Sunway University)

Abstract

In this paper, we deal with a new class of SOS-convex (sum of squares convex) polynomial optimization problems with spectrahedral uncertainty data in both the objective and constraints. By using robust optimization and a weighted-sum scalarization methodology, we first present the relationship between robust solutions of this uncertain SOS-convex polynomial optimization problem and that of its corresponding scalar optimization problem. Then, by using a normal cone constraint qualification condition, we establish necessary and sufficient optimality conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem based on scaled diagonally dominant sums of squares conditions and linear matrix inequalities. Moreover, we introduce a semidefinite programming relaxation problem of its weighted-sum scalar optimization problem, and show that robust weakly efficient solutions of the uncertain SOS-convex polynomial optimization problem can be found by solving the corresponding semidefinite programming relaxation problem.

Suggested Citation

  • Xiangkai Sun & Jiayi Huang & Kok Lay Teo, 2024. "On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems," Journal of Global Optimization, Springer, vol. 88(3), pages 755-776, March.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:3:d:10.1007_s10898-023-01353-1
    DOI: 10.1007/s10898-023-01353-1
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    References listed on IDEAS

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    1. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    2. 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.
    3. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
    4. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    5. T. D. Chuong & V. Jeyakumar & G. Li, 2019. "A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs," Journal of Global Optimization, Springer, vol. 75(4), pages 885-919, December.
    6. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
    7. 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.
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    Cited by:

    1. Ilias Kotsireas & Panos Pardalos & Julius Žilinskas, 2024. "Preface," Journal of Global Optimization, Springer, vol. 88(3), pages 531-532, March.

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