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

作     者：Ma, Xuejie Yang, Sixing Liu, Pengjie Shen, Liang Li, Minze 

作者机构：Guangzhou Huashang Coll Sch Artificial Intelligence Guangzhou 511300 Peoples R China China Univ Min & Technol Sch Math Xuzhou 221116 Peoples R China Xuzhou Med Univ Sch Management Xuzhou 221004 Peoples R China Imperial Coll London Dept Math London SW7 2AZ England 

出 版 物：《JOURNAL OF APPLIED MATHEMATICS AND COMPUTING》 (J. Appl. Math. Comp.)

年 卷 期：2025年第71卷第3期

页      面：3087-3107页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China Guangzhou Huashang College Daoshi Project [2024HSDS15] Mathematics Tianyuan Fund of the National Natural Science Foundation of China [12326315, 12326321] Natural Science Foundation of Jiangsu Province [BK20230678] 

主　　题：Unconstrained optimization Spectral conjugate gradient method Restart feature Theoretical convergence Image restoration 

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.