凸约束方程组的新型无导数算法及在信号重构中的应用  

Novel Derivative-Free Algorithm for Convex Constrained Equations and Its Application in Signal Reconstruction

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

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

出　　处：《吉林大学学报（理学版）》2024年第6期1345-1351,共7页Journal of Jilin University:Science Edition

基　　金：广西自然科学基金(批准号:2024GXNSFAA010478);广州华商学院校内导师制项目(批准号:2023HSDS38).

摘　　要：提出一种新型无导数算法,以解决凸约束非线性方程组问题.该算法利用改进的共轭参数设计搜索方向,以确保算法的充分下降性和信赖域特性.在适当的假设下,该算法具有全局收敛性.数值仿真结果表明,该算法在处理凸约束非线性方程组问题和信号重构问题时具有高效性和鲁棒性.We proposed a novel derivative-free algorithm to solve convex constrained nonlinear equation systems.The algorithm utilized improved conjugate parameters to design a search direction,ensuring sufficient descent and trust region characteristics of the algorithm.Under appropriate assumptions,the algorithm had global convergence.Numerical simulation results show that the algorithm has high efficiency and robustness in handling convex constrained nonlinear equation systems and signal reconstruction problems.

关 键 词：凸约束非线性方程组 无导数 全局收敛性 信号重构 

分 类 号：O224[理学—运筹学与控制论]