求解广义Lyapunov方程的非单调谱投影梯度法  

Nonmonotone Spectral Projection Gradient Method for Solving Generalized Lyapunov Equations

作　　者：喻思婷 李春梅[1] 段雪峰[1] YU Si-ting;LI Chun-mei;DUAN Xue-feng(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004)

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《工程数学学报》2018年第6期673-683,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11561015;11761024);广西自然科学基金(2016GXNSFFA380009;2016GXNSFAA380074;2017GXNSFBA198082);广西密码学与信息安全重点实验室开放基金(GCIS201616)~~

摘　　要：本文研究双线性控制系统中的一类广义Lyapunov方程的半正定解.基于凸函数的局部极小解就是全局极小解这一良好性质,首先将广义Lyapunov方程的半正定解问题等价转化为凸优化问题.利用非单调线搜索技术确定步长,构造了非单调谱投影梯度方法求解这一等价问题.最后用数值例子验证了新方法的可行性和有效性.In this paper,we consider the positive semidefinite solution to a class of generalized Lyapunov matrix equation,which arises in bilinear systems.Based on the good property that the local minimizer of a convex function is also the global minimizer,the positive semidefinite solution of the generalized Lyapunov equation is transformed into a convex optimization problem.By using the nonmonotone line search technique,we develop a nonmonotone spectral projected gradient method to solve this equivalent problem.Finally,numerical examples are presented to illustrate the feasibility and effectiveness of the new method.

关 键 词：广义Lyapunov方程 半正定解 非单调线搜索 投影梯度方法 

分 类 号：O241.7[理学—计算数学]