Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions
Quadratic Growth Conditions for Convex Matrix Optimization Problems Associated with Spectral Functions
复制标题
与谱函数相关的凸矩阵优化问题的二次增长条件
DOI：
10.1137/17m1116325
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发表时间：
2017-02
影响因子：
3.1
通讯作者：
Zhao Xinyuan
中科院分区：
文献类型：
--
作者：
Cui Ying;Ding Chao;Zhao Xinyuan
在本文中，我们提供了两类充分条件，用于确保一类由非光滑谱函数正则化的约束凸对称和非对称矩阵优化问题的二次增长条件。这些充分（条件）……（最后一个单词不完整，可能影响整体语义理解）
In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and nonsymmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the $\mathcal{C}^2$-cone reducibility of spectral functions and the metric subregularity of their subdifferentials, respectively. As an application, we demonstrate how quadratic growth conditions are used to guarantee the desirable fast convergence rates of the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Numerical experiments on an easy-to-implement ALM applied to the fastest mixing Markov chain problem are also presented to illustrate the significance of the obtained results.
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凸复合规划乘子交替方向法的线性速率收敛
影响因子：
1.7
作者：
Deren Han;Defeng Sun;Liwei Zhang
通讯作者：
Liwei Zhang
DOI：
10.1007/b97543
发表时间：
2003
期刊：
--
影响因子：
--
作者：
F. Facchinei;J. Pang
通讯作者：
F. Facchinei;J. Pang
DOI：
10.1287/moor.1060.0195
发表时间：
2006-11
期刊：
Math. Oper. Res.
影响因子：
--
作者：
Defeng Sun
通讯作者：
Defeng Sun
影响因子：
22.7
作者：
Candes, Emmanuel;Recht, Benjamin
通讯作者：
Recht, Benjamin
影响因子：
0.5
作者：
Boyd, S;Diaconis, P;Xiao, L
通讯作者：
Xiao, L