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Optimality Conditions and Duality in Nonsmooth Adjustable Robust Optimization Problems

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  • Mai Van Duy

    (University of Science, Vietnam National University
    FPT University)

  • Phan Quoc Khanh

    (Faculty of Mathematics and Statistics, Ton Duc Thang University)

  • Nguyen Minh Tung

    (Ho Chi Minh University of Banking)

Abstract

In this paper, we consider nonsmooth adjustable robust optimization problems and necessary/sufficient conditions based on qualification conditions and generalized convexity concepts. Verifiable sufficient conditions and useful relations for these qualification conditions are provided. Our analysis covers a wide range of uncertain sets commonly used in adjustable robust optimization, and we employ a dual approach to address non-reformulated cases of uncertain set, while also providing a direct approach to these problems through reformulation.

Suggested Citation

  • Mai Van Duy & Phan Quoc Khanh & Nguyen Minh Tung, 2025. "Optimality Conditions and Duality in Nonsmooth Adjustable Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-28, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02818-x
    DOI: 10.1007/s10957-025-02818-x
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