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Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications

Author

Listed:
  • Cao Thanh Tinh

    (Vietnam National University
    University of Information Technology)

  • Thai Doan Chuong

    (Saigon University
    RMIT University)

Abstract

In this paper, we first present strong conic linear programming duals for convex quadratic semi-infinite problems with linear constraints and geometric index sets. The obtained results show that the optimal values of a convex quadratic semi-infinite problem with convex compact sets and its associated conic linear programming dual problem are equal with the solution attainment of the dual program. We then prove that the conic linear programming dual is equivalently reformulated as a second-order cone programming problem whenever the index sets are ellipsoids, balls, cross-polytopes or boxes. As an application, we show that a class of separable fractional quadratic semi-infinite programs also admits second-order cone programming duality under ellipsoidal index sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:2:d:10.1007_s10957-022-02040-z
    DOI: 10.1007/s10957-022-02040-z
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    References listed on IDEAS

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    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. Li Wang & Feng Guo, 2014. "Semidefinite relaxations for semi-infinite polynomial programming," Computational Optimization and Applications, Springer, vol. 58(1), pages 133-159, May.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
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    Cited by:

    1. Xiangkai Sun & Wen Tan & Kok Lay Teo, 2023. "Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 737-764, May.
    2. 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.

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