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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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