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<p>In this paper, we introduce and study new notions of <i>directional Levitin–Polyak well-posedness</i> for both optimization problems and variational inequalities. First, we establish necessary and sufficient conditions for these directional Levitin–Polyak well-posednesses. Then, we show a close relationship between the directional Levitin–Polyak well-posedness of optimization problems and that of variational inequalities. In addition, we present several examples to illustrate the advantages of our results over existing ones in the literature.</p>

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Directional Levitin–Polyak well-posedness for optimization problems and variational inequalities

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Do Sang Kim,
  • Kwan Deok Bae,
  • Vo Si Trong Long

摘要

In this paper, we introduce and study new notions of directional Levitin–Polyak well-posedness for both optimization problems and variational inequalities. First, we establish necessary and sufficient conditions for these directional Levitin–Polyak well-posednesses. Then, we show a close relationship between the directional Levitin–Polyak well-posedness of optimization problems and that of variational inequalities. In addition, we present several examples to illustrate the advantages of our results over existing ones in the literature.