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<p>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.</p>

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Solution Existence and Compactness Analysis for Nonsmooth Optimization Problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月3日

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  • Nguyen Canh Hung,
  • Thai Doan Chuong,
  • Nguyen Le Hoang Anh

摘要

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.