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Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

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  • Nguyen Canh Hung

    (University of Science
    Vietnam National University
    Nha Trang University)

  • Thai Doan Chuong

    (Brunel University London)

  • Nguyen Le Hoang Anh

    (University of Science
    Vietnam National University)

Abstract

In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.

Suggested Citation

  • Nguyen Canh Hung & Thai Doan Chuong & Nguyen Le Hoang Anh, 2024. "Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 771-794, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02447-w
    DOI: 10.1007/s10957-024-02447-w
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    References listed on IDEAS

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    1. 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.
    2. Chieu, N.H. & Jeyakumar, V. & Li, G. & Mohebi, H., 2018. "Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation," European Journal of Operational Research, Elsevier, vol. 265(1), pages 19-25.
    3. E. Allevi & J. E. Martínez-Legaz & R. Riccardi, 2020. "Optimality conditions for convex problems on intersections of non necessarily convex sets," Journal of Global Optimization, Springer, vol. 77(1), pages 143-155, May.
    4. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, December.
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