非线性方程组的方向重启改进型算法及应用  

Directional Restart Improvement Algorithm for Nonlinear Equation Systems and Its Application

作　　者：夏艳 李丹丹 王松华 李远飞 XIA Yan;LI Dandan;WANG Songhua;LI Yuanfei(Department of Applied Mathematics,Guangzhou Huashang College,Guang zhou 511300,China;School of Mathematics and Statistics,Baise University,Baise 533000,China)

机构地区：[1]广州华商学院应用数学系,广东广州511300 [2]百色学院数学与统计学院,广西百色533000

出　　处：《北华大学学报（自然科学版）》2024年第6期708-713,共6页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(11371175);广西自然科学基金项目(2024GXNSFAA010478,2020GANSFAA159069);广州华商学院导师制项目(2023HSDS38)。

摘　　要：提出一种方向重启改进的共轭梯度算法,旨在优化凸约束非线性方程组和稀疏信号恢复问题的求解过程。通过修正经典的共轭参数设计新的搜索方向,并结合投影技术与无导数线搜索技术来更新迭代点。新的搜索方向在不依赖于任何线搜索下具备充分下降性与信赖域特征,且在合理的假设下证明了新算法的全局收敛性质。数值实验结果表明,新算法在求解凸约束非线性方程组和信号恢复的应用场景中,相比同类算法具有更优的性能和更广泛的应用潜力。A directional restart improvement conjugate gradient algorithm is presented,aiming at optimizing convex-constrained nonlinear equation systems and sparse signal recovery problems.A new search direction is designed by modifying the classical conjugate parameters,and the integration of projection techniques and derivative-free line search methods is used to update iteration points.The new search direction,independent of any line search,possesses sufficient descent properties and trust-region features,and the global convergence properties of the new algorithm has been proven under reasonable assumptions.Numerical experiments show that the new algorithm has superior performance and broader application potential for solving convex-constrained nonlinear equation systems and signal recovery scenarios comparing to similar algorithms.

关 键 词：大规模凸约束非线性方程组 共轭梯度法 全局收敛性 信号恢复 

分 类 号：O224[理学—运筹学与控制论]