一类求解大规模非线性单调方程组的无导数共轭梯度方法  

A New Derivative-free Conjugate Gradient Type Method for Large-scale Nonlinear Systems of Monotone Equations

作　　者：李艳冉 高静[1] 曹名圆[1] 姜晓威[1] 白雪 LI Yanran;GAO Jing;CAO Mingyuan;JIANG Xiaowei;BAI Xue(Mathematical and Stastistical College of Beihua University,Jilin 132013,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《北华大学学报（自然科学版）》2021年第1期15-20,共6页Journal of Beihua University（Natural Science）

基　　金：吉林省科技发展计划项目(2020122367JC);吉林省教育厅科学技术研究项目(JJKH20200028KJ);北华大学青年培育计划项目(2017QNJJL10);北华大学研究生创新计划项目(2019043).

摘　　要：提出一类求解大规模非线性单调方程组的无导数共轭梯度算法.利用Liu和Feng提出的共轭参数改进技术,对数值性能较优越的RMIL共轭梯度方向进行改进,并引入谱参数,构造新的搜索方向.该方向继承了RMIL共轭梯度法的数值稳定性且满足充分下降性条件.再结合投影技术和无导数线搜索技术,在适当假设条件下,获得算法的全局收敛性证明.数值结果表明,该算法在求解大规模非线性单调方程组时具有明显优势.A new derivative-free conjugate gradient type algorithm for large-scale nonlinear systems of monotone equations is presented.The RMIL conjugate gradient direction with superior numerical performance is improved by using the conjugate parameter improvement technology proposed by Liu and Feng,and a new search direction is constructed by introducing spectral parameter.This direction inherits the numerical stability of RMIL conjugate gradient method and satisfies the sufficient descent condition.The method combines the hyperplane projection and the derivative-free line search technique to compute the iteration points.Under some appropriate assumptions,the global convergence of the given methods is established.Numerical experiments indicate that the proposed method is effective.

关 键 词：无导数技术 非线性单调方程组 投影技术 共轭梯度法 

分 类 号：O224[理学—运筹学与控制论]