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Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems

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  • Thai Doan Chuong

    (Saigon University)

  • José Vicente-Pérez

    (Universidad de Alicante)

Abstract

In this paper, we examine stable exact relaxations for classes of parametric robust convex polynomial optimization problems under affinely parameterized data uncertainty in the constraints. We first show that a parametric robust convex polynomial problem with convex compact uncertainty sets enjoys stable exact conic relaxations under the validation of a characteristic cone constraint qualification. We then show that such stable exact conic relaxations become stable exact semidefinite programming relaxations for a parametric robust SOS-convex polynomial problem, where the uncertainty sets are assumed to be bounded spectrahedra. In addition, under the corresponding constraint qualification, we derive stable exact second-order cone programming relaxations for some classes of parametric robust convex quadratic programs under ellipsoidal uncertainty sets.

Suggested Citation

  • Thai Doan Chuong & José Vicente-Pérez, 2023. "Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 387-410, May.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:2:d:10.1007_s10957-023-02197-1
    DOI: 10.1007/s10957-023-02197-1
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    References listed on IDEAS

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    1. Chuong, T.D. & Jeyakumar, V., 2017. "Convergent hierarchy of SDP relaxations for a class of semi-infinite convex polynomial programs and applications," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 381-399.
    2. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    3. 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.
    4. 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.
    5. 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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