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<p>Using the normal-<i>S</i> iterative method [D.R. Sahu, <i>Fixed Point Theory</i> <b>12</b> (2011), 187–204], a gradient projection algorithm for solving convex minimization problems in Hilbert spaces is designed. A rigorous analysis of the convergence properties of the proposed algorithm is given, establishing strong convergence results through systematic refinement. The theoretical advancements are supported by non-trivial examples and comprehensive numerical experiments on benchmark datasets, demonstrating a superior computational efficiency of our algorithms, as well as their accuracy and convergence. Our findings significantly improve upon the outcomes of earlier studies.</p>

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A gradient projection algorithm based on the normal-S iterative algorithm: convergence analysis and machine learning application

  • 期刊论文

  • 发表日期：

    2025年8月19日

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  • Müzeyyen Ertürk,
  • Faik Gürsoy,
  • Emirhan Hacıoğlu,
  • Gradimir V. Milovanović

摘要

Using the normal-S iterative method [D.R. Sahu, Fixed Point Theory 12 (2011), 187–204], a gradient projection algorithm for solving convex minimization problems in Hilbert spaces is designed. A rigorous analysis of the convergence properties of the proposed algorithm is given, establishing strong convergence results through systematic refinement. The theoretical advancements are supported by non-trivial examples and comprehensive numerical experiments on benchmark datasets, demonstrating a superior computational efficiency of our algorithms, as well as their accuracy and convergence. Our findings significantly improve upon the outcomes of earlier studies.