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A Unifying Approach to Robust Convex Infinite Optimization Duality

Author

Listed:
  • Nguyen Dinh

    (International University, Vietnam National University)

  • Miguel Angel Goberna

    (University of Alicante)

  • Marco Antonio López

    (University of Alicante
    Federation University)

  • Michel Volle

    (Avignon University)

Abstract

This paper considers an uncertain convex optimization problem, posed in a locally convex decision space with an arbitrary number of uncertain constraints. To this problem, where the uncertainty only affects the constraints, we associate a robust (pessimistic) counterpart and several dual problems. The paper provides corresponding dual variational principles for the robust counterpart in terms of the closed convexity of different associated cones.

Suggested Citation

  • Nguyen Dinh & Miguel Angel Goberna & Marco Antonio López & Michel Volle, 2017. "A Unifying Approach to Robust Convex Infinite Optimization Duality," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 650-685, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1136-x
    DOI: 10.1007/s10957-017-1136-x
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    References listed on IDEAS

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    1. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    2. V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
    3. Yanjun Wang & Ruizhi Shi & Jianming Shi, 2015. "Duality and robust duality for special nonconvex homogeneous quadratic programming under certainty and uncertainty environment," Journal of Global Optimization, Springer, vol. 62(4), pages 643-659, August.
    4. Jeyakumar, V. & Li, G.Y. & Srisatkunarajah, S., 2013. "Strong duality for robust minimax fractional programming problems," European Journal of Operational Research, Elsevier, vol. 228(2), pages 331-336.
    5. Suzuki, Satoshi & Kuroiwa, Daishi & Lee, Gue Myung, 2013. "Surrogate duality for robust optimization," European Journal of Operational Research, Elsevier, vol. 231(2), pages 257-262.
    6. Bram L. Gorissen & Hans Blanc & Dick den Hertog & Aharon Ben-Tal, 2014. "Technical Note---Deriving Robust and Globalized Robust Solutions of Uncertain Linear Programs with General Convex Uncertainty Sets," Operations Research, INFORMS, vol. 62(3), pages 672-679, June.
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