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<p>In this study, we present a spectral conjugate gradient method with a built-in restart feature tailored for unconstrained optimization problems. We introduce a selection of bounded spectral parameters, develop an innovative truncation strategy for the RMIL-type conjugate parameter, and establish a novel restart mechanism within our composite search direction. Regardless of the selected bounded spectral parameter and the line search employed, we demonstrate that our proposed search direction meets the sufficient descent property. Furthermore, we establish its global convergence under standard assumptions, including the use of the weak Wolfe line search to generate step size. Numerical comparisons with existing methods highlight the superior performance of our presented methods in addressing unconstrained optimization. Ultimately, we apply the method to solve image restoration problems.</p>

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Solving unconstrained optimization using a spectral CG method with restart feature and its application

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Xuejie Ma,
  • Sixing Yang,
  • Pengjie Liu,
  • Liang Shen,
  • Minze Li

摘要

In this study, we present a spectral conjugate gradient method with a built-in restart feature tailored for unconstrained optimization problems. We introduce a selection of bounded spectral parameters, develop an innovative truncation strategy for the RMIL-type conjugate parameter, and establish a novel restart mechanism within our composite search direction. Regardless of the selected bounded spectral parameter and the line search employed, we demonstrate that our proposed search direction meets the sufficient descent property. Furthermore, we establish its global convergence under standard assumptions, including the use of the weak Wolfe line search to generate step size. Numerical comparisons with existing methods highlight the superior performance of our presented methods in addressing unconstrained optimization. Ultimately, we apply the method to solve image restoration problems.