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<p>In this study, we investigate a nonsmooth and nonconvex optimization problem with an unbounded feasible set. Leveraging recent advancements in variational analysis at infinity, we establish novel necessary and sufficient optimality conditions formulated in terms of the normal cone and limiting subdifferentials at infinity. Moreover, by introducing newly defined sets, we analyze asymptotic conditions that ensure the existence and compactness of the solution set for the given optimization problem. Building upon the obtained results, we further investigate the stability of solutions to optimization problems.</p>

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Optimality conditions and solution analysis at infinity for nonsmooth optimization problems

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Nguyen Canh Hung,
  • Nguyen Le Hoang Anh

摘要

In this study, we investigate a nonsmooth and nonconvex optimization problem with an unbounded feasible set. Leveraging recent advancements in variational analysis at infinity, we establish novel necessary and sufficient optimality conditions formulated in terms of the normal cone and limiting subdifferentials at infinity. Moreover, by introducing newly defined sets, we analyze asymptotic conditions that ensure the existence and compactness of the solution set for the given optimization problem. Building upon the obtained results, we further investigate the stability of solutions to optimization problems.