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<p>The paper is devoted to the study of the Newton-type scheme applied to the problem of finding a solution to the inclusion governed by set-valued mappings. We develop a stability result for global metric regularity and use it to investigate the semilocal convergence for the Josephy-Newton framework. On the other hand, we investigate in the second fold of the paper the behavior of iterative process based on Josephy-Newton scheme for solving variational problems involving convex processes.</p>

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Restrictive metric regularity of set-valued mappings and applications to the Newton’s method for generalized equations

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Van Vu Nguyen,
  • Van Ngai Huynh

摘要

The paper is devoted to the study of the Newton-type scheme applied to the problem of finding a solution to the inclusion governed by set-valued mappings. We develop a stability result for global metric regularity and use it to investigate the semilocal convergence for the Josephy-Newton framework. On the other hand, we investigate in the second fold of the paper the behavior of iterative process based on Josephy-Newton scheme for solving variational problems involving convex processes.