| 求解广义Lyapunov方程的非单调谱投影梯度法 |
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| 引用本文： | 喻思婷,李春梅,段雪峰.求解广义Lyapunov方程的非单调谱投影梯度法[J].工程数学学报,2018,35(6):673-683. |
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| 作者姓名： | 喻思婷 李春梅 段雪峰 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院， 桂林541004 |
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| 基金项目： | 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). |
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| 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．
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| 关 键 词： | 广义Lyapunov方程 半正定解 非单调线搜索 投影梯度方法 |
| 收稿时间： | 2016-12-01 |
Nonmonotone Spectral Projection Gradient Method for Solving Generalized Lyapunov Equations |
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| YU Si-ting,LI Chun-mei,DUAN Xue-feng.Nonmonotone Spectral Projection Gradient Method for Solving Generalized Lyapunov Equations[J].Chinese Journal of Engineering Mathematics,2018,35(6):673-683. |
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| Authors: | YU Si-ting LI Chun-mei DUAN Xue-feng |
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| Affiliation: | School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004 |
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| Abstract: | 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. |
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| Keywords: | generalized Lyapunov equation positive semidefinite solution nonmonotone line search projected gradient method |
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