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Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems

Author

Listed:
  • Nguyen Canh Hung

    (University of Science
    Vietnam National University)

  • Thai Doan Chuong

    (Brunel University of London)

  • Nguyen Le Hoang Anh

    (University of Science
    Vietnam National University)

Abstract

This paper is concerned with the analysis of geometrical properties and behaviors of the optimal value and global optimal solutions for a class of nonsmooth optimization problems. We provide conditions under which the solution set of a nonsmooth and nonconvex optimization problem is non-empty and/or compact. We also examine related properties such as the compactness of the sublevel sets, the boundedness from below and the coercivity of the objective function to characterize the non-emptiness and the compactness of the solution set of the underlying optimization problem under the unboundedness of its associated feasible set.

Suggested Citation

  • Nguyen Canh Hung & Thai Doan Chuong & Nguyen Le Hoang Anh, 2025. "Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-25, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02637-0
    DOI: 10.1007/s10957-025-02637-0
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    References listed on IDEAS

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    1. F. Flores-Bazán & N. Hadjisavvas & F. Lara & I. Montenegro, 2016. "First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 372-393, August.
    2. 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.
    3. Kazufumi Ito & Karl Kunisch, 2014. "A Note on the Existence of Nonsmooth Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 697-706, December.
    4. Alfred Auslender, 1996. "Noncoercive Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 769-782, November.
    5. A. E. Ozdaglar & P. Tseng, 2006. "Existence of Global Minima for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 523-546, March.
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