Scholarlink

<p>In this paper, we provide an account of some fast iterative algorithms for variational inequalities that are robust with respect to unknown Lipschitz constant. We propose two self-adaptive double inertial algorithms for solving <i>Fichera-Stampacchia</i>-type variational inequality, accelerating the rate of convergence without assuming the knowledge of the Lipschitz constant as it is rarely known in practice. Surprisingly, both algorithms turn out to be well robust assuming only one orthogonal projection per iteration in compared to commonly used algorithms. For a proof of principle, we elaborate that under some mild conditions both algorithms converge strongly and weakly to an element of the solution set. In particular, we prove that under imposing strong pseudomonotonicity and Lipschitz continuity conditions both algorithms nicely converge strongly with an R-linearly rate of convergence. Finally, to support our theoretical results some numerical experiments with applications emphasized on optimal control problems are outlined. Mainly, the performance of the proposed algorithms is compared with other known methods in the literature.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Self-Adaptive Double Inertial Schemes for Variational Inequalities with Applications to Optimal Control Problems

  • 期刊论文

  • 发表日期：

    2025年8月17日

查看全文
  • Fridoun Moradlou,
  • Mahsa Mohammadpour

摘要

In this paper, we provide an account of some fast iterative algorithms for variational inequalities that are robust with respect to unknown Lipschitz constant. We propose two self-adaptive double inertial algorithms for solving Fichera-Stampacchia-type variational inequality, accelerating the rate of convergence without assuming the knowledge of the Lipschitz constant as it is rarely known in practice. Surprisingly, both algorithms turn out to be well robust assuming only one orthogonal projection per iteration in compared to commonly used algorithms. For a proof of principle, we elaborate that under some mild conditions both algorithms converge strongly and weakly to an element of the solution set. In particular, we prove that under imposing strong pseudomonotonicity and Lipschitz continuity conditions both algorithms nicely converge strongly with an R-linearly rate of convergence. Finally, to support our theoretical results some numerical experiments with applications emphasized on optimal control problems are outlined. Mainly, the performance of the proposed algorithms is compared with other known methods in the literature.