解无约束优化问题的一种新的谱梯度方法  

A New Spectral Gradient Method for Unconstrained Optimization

作　　者：周群艳 ZHOU Qunyan(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,China)

机构地区：[1]江苏理工学院数理学院,江苏常州213001

出　　处：《应用数学》2020年第4期857-868,共12页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11471145)。

摘　　要：本文提出一种解大规模无约束非线性优化问题的利用新的非单调策略的修正谱梯度方法.这种方法借助广义弱拟牛顿方程来计算初始步长.在合理的假设条件下,新算法全局收敛.初步数值结果表明新方法是有效且有竞争力的.A modified spectral gradient method of using a new nonmonotone strategy for solving large scale unconstrained nonlinear optimization problems is proposed. The computation of the initial stepsize is based on use of the generalized weak quasi-Newton equation. Under some reasonable conditions, the global convergence of the proposed algorithm is established. Preliminary numerical results and comparisons indicate that the new method is efficient and competitive.

关 键 词：谱梯度方法 弱拟牛顿方程 非单调线搜索 全局收敛 

分 类 号：O224[理学—运筹学与控制论]