Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems

Nguyen Canh Hung (), Thai Doan Chuong () and Nguyen Le Hoang Anh ()
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Nguyen Canh Hung: University of Science
Thai Doan Chuong: Brunel University of London
Nguyen Le Hoang Anh: University of Science

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 1, No 18, 25 pages

Abstract: 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.

Keywords: Solution existence; Limiting subdifferential; Nonsmooth optimization; Coercivity; Compactness; 65K10; 49K99; 90C46; 90C29 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02637-0

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