一类带凸约束的单调非线性方程组的无导数投影法收敛率分析  

Convergence Rate Analysis of a Class of Derivative-Free Projection Methods for Convex Constrained Monotone Nonlinear Equations

作　　者：李琳 林海婵 欧宜贵[1] LI Lin;LIN Haichan;OU Yigui(School of Science,Hainan University,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228

出　　处：《应用数学》2021年第4期940-949,共10页Mathematica Applicata

基　　金：Supported by NNSF(11961018);NSF of Hainan Province (120QN175)。

摘　　要：在适当的条件下,本文进一步研究带凸约束的单调非线性方程组的超记忆梯度型方法,并建立了它的次线性收敛率.同时,本文还给出求解带凸约束的单调非线性方程组的无导数投影法的更一般的算法框架,并分析了其收敛性及其收敛率.两个说明性的数值计算实例表明了该算法框架的可行性.In this paper, we further study the existing supermemory gradient-type method for solving convex constrained monotone nonlinear equations and establish its sub-linear convergence rate under some mild conditions. Furthermore, a more general algorithmic framework of derivative-free projection method for solving convex constrained nonlinear monotone equations is proposed and its convergence properties are discussed.Two illustrative examples are reported to verify the feasibility of the proposed algorithmic framework.

关 键 词：非线性方程组 单调性 投影方法 收敛率分析 

分 类 号：O221[理学—运筹学与控制论]