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<p>In this paper, we propose a new relaxed self-adaptive alternating inertial algorithm for solving variational inequality problem with the multiple-sets split feasibility problem with multiple output sets constraint. Under some suitable conditions on the control parameters, without the consideration of the knowledge of the operator norm, and assuming that the cost operators are pseudomonotone and non-Lipschitz, we prove that the sequence generated by the proposed algorithm converges strongly to a minimum-norm element of the solution of the problem in the setting of Hilbert spaces. In order to improve the convergence properties of the proposed algorithm, we employ the relaxation method as well as the alternating inertial technique. Finally, We illustrate the convergence of the proposed algorithm using numerical examples.</p>

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Relaxed self-adaptive alternating inertial algorithm for solving variational inequalities with the multiple-sets split feasibility problem with multiple output sets constraint

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Solomon Gebregiorgis,
  • Poom Kumam

摘要

In this paper, we propose a new relaxed self-adaptive alternating inertial algorithm for solving variational inequality problem with the multiple-sets split feasibility problem with multiple output sets constraint. Under some suitable conditions on the control parameters, without the consideration of the knowledge of the operator norm, and assuming that the cost operators are pseudomonotone and non-Lipschitz, we prove that the sequence generated by the proposed algorithm converges strongly to a minimum-norm element of the solution of the problem in the setting of Hilbert spaces. In order to improve the convergence properties of the proposed algorithm, we employ the relaxation method as well as the alternating inertial technique. Finally, We illustrate the convergence of the proposed algorithm using numerical examples.