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<p>This paper investigates four adaptive projection and contraction algorithms with double inertial extrapolation steps for finding common solutions of variational inequalities governed by quasimonotone operators and fixed point problems involving demicontractive mappings in real Hilbert spaces. The proposed algorithms employ two distinct step sizes at each iteration and incorporate a nonmonotone step size criterion. The strong convergence of the generated sequences is established under suitable assumptions. Numerical experiments in both finite- and infinite-dimensional settings, including an application in signal processing, are provided to demonstrate the effectiveness of the proposed methods.</p>

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Four double inertial algorithms for variational inequalities with fixed point constraints: theory and signal processing applications

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Shanshan Xu,
  • Songxiao Li,
  • Jen-Chih Yao

摘要

This paper investigates four adaptive projection and contraction algorithms with double inertial extrapolation steps for finding common solutions of variational inequalities governed by quasimonotone operators and fixed point problems involving demicontractive mappings in real Hilbert spaces. The proposed algorithms employ two distinct step sizes at each iteration and incorporate a nonmonotone step size criterion. The strong convergence of the generated sequences is established under suitable assumptions. Numerical experiments in both finite- and infinite-dimensional settings, including an application in signal processing, are provided to demonstrate the effectiveness of the proposed methods.