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<p>In this paper, we propose three kinds of self-adaptive proximal gradient algorithms with inertial steps for solving convex bilevel optimization problems. Firstly, under reasonable parameters, we prove that the sequences generated by the proposed algorithms converge strongly to some solution of the problem, which is the unique solution of some variational inequality problem. Secondly, we extend three inertial self-adaptive algorithms to multi-step inertial versions. Finally, in the numerical experiments, we illustrate the performance of our algorithms and present some comparisons with related algorithms.</p>

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Inertial self-adaptive methods for solving convex bilevel problems

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Jiajun Guo,
  • Peichao Duan

摘要

In this paper, we propose three kinds of self-adaptive proximal gradient algorithms with inertial steps for solving convex bilevel optimization problems. Firstly, under reasonable parameters, we prove that the sequences generated by the proposed algorithms converge strongly to some solution of the problem, which is the unique solution of some variational inequality problem. Secondly, we extend three inertial self-adaptive algorithms to multi-step inertial versions. Finally, in the numerical experiments, we illustrate the performance of our algorithms and present some comparisons with related algorithms.