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Solution existence for a class of nonsmooth robust optimization problems

Author

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  • Nguyen Canh Hung

    (University of Science
    Vietnam National University
    Nha Trang University)

  • Thai Doan Chuong

    (Brunel University of London)

  • Nguyen Hoang Anh

    (Vietnam National University
    University of Science)

Abstract

The main purpose of this paper is to investigate the existence of global optimal solutions for nonsmooth and nonconvex robust optimization problems. To do this, we first introduce a concept called extended tangency variety and show how a robust optimization problem can be transformed into a minimizing problem of the corresponding tangency variety. We utilize this concept together with a constraint qualification condition and the boundedness of the objective function to provide relationships among the concepts of robust properness, robust M-tamesness and robust Palais-Smale condition related to the considered problem. The obtained results are also employed to derive necessary and sufficient conditions for the existence of global optimal solutions to the underlying robust optimization problem.

Suggested Citation

  • Nguyen Canh Hung & Thai Doan Chuong & Nguyen Hoang Anh, 2025. "Solution existence for a class of nonsmooth robust optimization problems," Journal of Global Optimization, Springer, vol. 92(1), pages 111-133, May.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:1:d:10.1007_s10898-024-01450-9
    DOI: 10.1007/s10898-024-01450-9
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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. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    3. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
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