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<p>In this paper, we introduce two new iterative methods based on the viscosity and modified Mann methods, for solving a general class of inclusion problem which contains the fixed point of a quasi-pseudocontractive operator. Our methods are fully self-adaptive, void of any linesearch procedure, and do not require prior knowledge of the Lipschitz constant of the monotone operator. We prove strong and <i>R</i>-linear convergence theorems for our proposed methods, and apply our result in solving variational inequality and optimal control problems. Finally, we conduct performance profile of our methods in comparison with related methods in the literature.</p>

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Efficient algorithms for solving a class of generalized inclusion problem with application to optimal control

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Oluwatosin T. Mewomo,
  • Victor A. Uzor,
  • Ephraim Agyingi,
  • Blessing O. Emerenini

摘要

In this paper, we introduce two new iterative methods based on the viscosity and modified Mann methods, for solving a general class of inclusion problem which contains the fixed point of a quasi-pseudocontractive operator. Our methods are fully self-adaptive, void of any linesearch procedure, and do not require prior knowledge of the Lipschitz constant of the monotone operator. We prove strong and R-linear convergence theorems for our proposed methods, and apply our result in solving variational inequality and optimal control problems. Finally, we conduct performance profile of our methods in comparison with related methods in the literature.