Scholarlink

<p>In this paper, we first improve the Hager-Zhang conjugate parameter [SIAM J. Optim., 16(1):170-192, 2005], utilize the Dai-Liao conjugacy condition and the quasi-Newton direction to determine the spectral parameter in the search direction, and then introduce a new restart mechanism, which includes a flexible non-negative vector, to construct a composite search direction that automatically satisfies the sufficient descent and trust region properties. Combining this with the hybrid-inertial accelerated technique and the hyperplane projection approach, we propose a hybrid-inertial accelerated spectral conjugate gradient projection method for solving the unconstrained pseudo-monotone system of nonlinear equations. Unlike most existing inertial acceleration strategies, the proposed method incorporates a hybrid-inertial acceleration technique, which utilizes multiple previous iterations and generates inertial iterative points in two different ways. The proposed method is demonstrated to achieve global convergence without assuming Lipschitz continuity. Furthermore, under the assumption of locally Lipschitz continuity, a comprehensive analysis is conducted to evaluate both the asymptotic and non-asymptotic global convergence rates in terms of iteration complexity. Numerical experiments demonstrate the effectiveness of the proposed method for solving eleven unconstrained systems of nonlinear equations. Finally, its potential applications are illustrated through compressed sensing problems, including signal recovery and image restoration.</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

A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing

  • 期刊论文

  • 发表日期：

    2025年4月30日

查看全文
  • Linhao Li,
  • Pengjie Liu,
  • Hu Shao,
  • Bohan Li

摘要

In this paper, we first improve the Hager-Zhang conjugate parameter [SIAM J. Optim., 16(1):170-192, 2005], utilize the Dai-Liao conjugacy condition and the quasi-Newton direction to determine the spectral parameter in the search direction, and then introduce a new restart mechanism, which includes a flexible non-negative vector, to construct a composite search direction that automatically satisfies the sufficient descent and trust region properties. Combining this with the hybrid-inertial accelerated technique and the hyperplane projection approach, we propose a hybrid-inertial accelerated spectral conjugate gradient projection method for solving the unconstrained pseudo-monotone system of nonlinear equations. Unlike most existing inertial acceleration strategies, the proposed method incorporates a hybrid-inertial acceleration technique, which utilizes multiple previous iterations and generates inertial iterative points in two different ways. The proposed method is demonstrated to achieve global convergence without assuming Lipschitz continuity. Furthermore, under the assumption of locally Lipschitz continuity, a comprehensive analysis is conducted to evaluate both the asymptotic and non-asymptotic global convergence rates in terms of iteration complexity. Numerical experiments demonstrate the effectiveness of the proposed method for solving eleven unconstrained systems of nonlinear equations. Finally, its potential applications are illustrated through compressed sensing problems, including signal recovery and image restoration.