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<p>This study examines the well-posedness and generalized well-posedness of variational-like inequality problems governed by a bifunction <i>h</i>, within the framework of higher-order strong invariant monotonicity. The key contribution is a two-step approach: well-posedness characterizations are first obtained for a Minty-type problem perturbed by a norm term tailored to the higher-order structure, and these results are then used to derive corresponding characterizations for the unperturbed Stampacchia formulation via higher-order strong invariant monotonicity. The Stampacchia analysis employs a modified approximating sequence with an embedded norm term, ensuring consistency with the perturbed Minty framework. We further introduce higher-order strong <i>h</i>-invexity and its generalizations, relate them to corresponding notions of strong invariant monotonicity, and use these concepts to connect the solutions of Stampacchia- and Minty-type problems with higher-order strict minimizers of a scalar optimization problem.</p>

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On the well-posedness of variational-like inequality problems involving bifunctions

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Monika Mehta,
  • Guneet Bhatia,
  • Ruchi Kaur

摘要

This study examines the well-posedness and generalized well-posedness of variational-like inequality problems governed by a bifunction h, within the framework of higher-order strong invariant monotonicity. The key contribution is a two-step approach: well-posedness characterizations are first obtained for a Minty-type problem perturbed by a norm term tailored to the higher-order structure, and these results are then used to derive corresponding characterizations for the unperturbed Stampacchia formulation via higher-order strong invariant monotonicity. The Stampacchia analysis employs a modified approximating sequence with an embedded norm term, ensuring consistency with the perturbed Minty framework. We further introduce higher-order strong h-invexity and its generalizations, relate them to corresponding notions of strong invariant monotonicity, and use these concepts to connect the solutions of Stampacchia- and Minty-type problems with higher-order strict minimizers of a scalar optimization problem.