Scholarlink

<p>In this paper, we first employ a hybrid technique and a flexible nonzero vector to design an effective restart direction, which is then incorporated into the search directions of the Fletcher-Reeves and Dai-Yuan methods, resulting in two improved methods for solving unconstrained optimization problems. For each improved method, we ensure that the corresponding search direction is independent of any line search, satisfies the sufficient descent condition, and possesses the trust region property. We establish the theoretical convergence of these methods under general conditions, including the use of a weak Wolfe line search for step size determination. Furthermore, by employing the Armijo line search for step size selection, we derive the iteration complexity of the improved methods. To assess their effectiveness, we apply the improved methods to solve unconstrained test problems and use performance profiles to present the numerical results. Finally, we apply the improved methods to image restoration problems to demonstrate their practical potential.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Improved Fletcher–Reeves and Dai–Yuan conjugate gradient methods with an efficient restart mechanism and their iterative complexity guarantees

  • 期刊论文

  • 发表日期：

    2025年7月24日

查看全文
  • Kai Wang,
  • Jiazheng Xi,
  • Pengjie Liu,
  • Chuang Yang

摘要

In this paper, we first employ a hybrid technique and a flexible nonzero vector to design an effective restart direction, which is then incorporated into the search directions of the Fletcher-Reeves and Dai-Yuan methods, resulting in two improved methods for solving unconstrained optimization problems. For each improved method, we ensure that the corresponding search direction is independent of any line search, satisfies the sufficient descent condition, and possesses the trust region property. We establish the theoretical convergence of these methods under general conditions, including the use of a weak Wolfe line search for step size determination. Furthermore, by employing the Armijo line search for step size selection, we derive the iteration complexity of the improved methods. To assess their effectiveness, we apply the improved methods to solve unconstrained test problems and use performance profiles to present the numerical results. Finally, we apply the improved methods to image restoration problems to demonstrate their practical potential.