An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update

Xiaoyu Wu (), Hu Shao (), Pengjie Liu () and Yue Zhuo ()
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Xiaoyu Wu: China University of Mining and Technology
Hu Shao: China University of Mining and Technology
Pengjie Liu: China University of Mining and Technology
Yue Zhuo: China University of Mining and Technology

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 3, No 10, 1130-1155

Abstract: Abstract Combining the derivative-free projection with inertial technique, we propose a hybrid inertial spectral conjugate gradient projection method for solving constrained nonlinear monotone equations. The conjugate parameter is a hybrid modification based on the memoryless BFGS update. The spectral parameter is obtained from quasi-Newton equations and double-truncated to ensure the sufficient descent. The search direction with a restart procedure satisfies sufficient descent condition and the trust region property at each iteration, independent of the choice of line search. We also investigate the theoretical properties, such as the global convergence and linear convergence rate, of the inertial projection method under normal assumptions. Numerical performances indicate the superiority of the proposed method in solving large-scale equations and restoring the blurred images contaminated by the Gaussian noise.

Keywords: Nonlinear monotone equations; Conjugate gradient projection method; Inertial step; Global convergence; Image restoration; 65K05; 90C56 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02265-6

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