求解非线性凸约束方程组问题的谱梯度型无导数投影算法及其应用  

A SPECTRAL GRADIENT-TYPE DERIVATIVE-FREE PROJECTION ALGORITHM FOR SOLVING NONLINEAR CONVEX CONSTRAINED EQUATIONS WITH ITS APPLICATION

作　　者：张宁 刘金魁[1] Zhang Ning;LiuJinkui(College of Mathematics and Statistics,Chongqing Three Gorges University,Wanzhou 404100,China)

机构地区：[1]重庆三峡学院数学与统计学院,万州404100

出　　处：《计算数学》2024年第2期173-188,共16页Mathematica Numerica Sinica

基　　金：重庆市自然科学基金面上项目(cstc2021jcyj-msxmX0233);重庆市研究生科研创新项目(CYS23735)资助.

摘　　要：基于SR1方法和谱共轭梯度方法,借助投影算子,本文建立了一种求解非线性凸约束单调方程组问题的谱梯度型无导数投影算法,其搜索方向满足充分下降性且独立于线搜索条件。在适当的假设条件下,算法具有全局收敛性.算例实验结果表明,该算法具有稳定性和有效性.最后,将算法应用于稀疏信号恢复问题.Based on the structures of SRl method and spectral conjugate gradient method,by using projection operator,we propose a spectral gradient-type derivative-free projection algorithm for solving nonlinear monotone equations with convex constraints.Its search direction satisfies the sufficient descent property which is independent of line search condition.The algorithm converges under some appropriate assumptions.The experimental results show that the algorithm is robust and effective.Finally,the algorithm is used to recover the sparse signal.

关 键 词：非线性方程组 无导数投影法 SR1校正法 全局收敛 信号恢复 

分 类 号：O224[理学—运筹学与控制论]