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<p>In this paper, we first employ a hybrid technique to modify the denominator of the Polak-Ribière-Polyak (PRP) conjugate parameter while keeping the numerator unchanged, to retain the self-adaptive restart property of the PRP method. Then, we develop a hybrid three-term conjugate gradient method that consistently satisfies the sufficient descent property for solving unconstrained optimization problems. Under general assumptions, including the use of a weak Wolfe line search for step size determination, we establish the theoretical convergence of the method. Additionally, by considering the Armijo line search for step size selection, we derive the iterative complexity of the method. Finally, we demonstrate the effectiveness of our proposed method through experiments on 100 unconstrained test problems and illustrate its practical potential by applying it to image restoration problems.</p>

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A Self-Adaptive Restarting Hybrid Three-Term Conjugate Gradient Method and its Applications

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Xuejie Ma,
  • Zhiyuan Xiang,
  • Jiawei Xu,
  • Pengjie Liu,
  • Ruixi Liu

摘要

In this paper, we first employ a hybrid technique to modify the denominator of the Polak-Ribière-Polyak (PRP) conjugate parameter while keeping the numerator unchanged, to retain the self-adaptive restart property of the PRP method. Then, we develop a hybrid three-term conjugate gradient method that consistently satisfies the sufficient descent property for solving unconstrained optimization problems. Under general assumptions, including the use of a weak Wolfe line search for step size determination, we establish the theoretical convergence of the method. Additionally, by considering the Armijo line search for step size selection, we derive the iterative complexity of the method. Finally, we demonstrate the effectiveness of our proposed method through experiments on 100 unconstrained test problems and illustrate its practical potential by applying it to image restoration problems.