国家自然科学基金(71271021)

作品数：4被引量：8H指数：2
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Global optimality condition and fixed point continuation algorithm for non-Lipschitz ?_p regularized matrix minimization被引量：2
《Science China Mathematics》2018年第6期1139-1152,共14页Dingtao Peng Naihua Xiu Jian Yu 
supported by National Natural Science Foundation of China(Grant Nos.11401124 and 71271021);the Scientific Research Projects for the Introduced Talents of Guizhou University(Grant No.201343);the Key Program of National Natural Science Foundation of China(Grant No.11431002)
Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identific...
关键词：lp regularized matrix minimization matrix completion problem p-thresholding operator globaloptimality condition fixed point continuation algorithm 
On Solutions of Sparsity Constrained Optimizatio被引量：4
《Journal of the Operations Research Society of China》2015年第4期421-439,共19页Li-Li Pan Nai-Hua Xiu Sheng-Long Zhou 
supported in part by the National Natural Science Foundation of China(Nos.11431002,71271021).
In this paper,we mainly study the existence of solutions to sparsity constrained optimization(SCO).Based on the expressions of tangent cone and normal cone of sparsity constraint,we present and characterize two first-...
关键词：Sparsity constrained optimization Tangent cone Normal cone First-order optimality condition Second-order optimality condition 
Half thresholding eigenvalue algorithm for semidefinite matrix completion
《Science China Mathematics》2015年第9期2015-2032,共18页CHEN YongQiang LUO ZiYan XIU NaiHua 
supported by National Natural Science Foundation of China(Grant Nos.11431002,71271021 and 11301022);the Fundamental Research Funds for the Central Universities of China(Grant No.2012YJS118)
The semidefinite matrix completion(SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, S...
关键词：semidefinite matrix completion S1/2relaxation half thresholding eigenvalue algorithm conver-gence 
Sparse and Low-Rank Covariance Matrix Estimation被引量：2
《Journal of the Operations Research Society of China》2015年第2期231-250,共20页Sheng-Long Zhou Nai-Hua Xiu Zi-Yan Luo Ling-Chen Kong 
The work was supported in part by the National Natural Science Foundation of China(Nos.11431002,11171018,71271021,11301022).
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices.We first benefit from a convex optimization which develops l1-norm penalty to encourage ...
关键词：Covariance matrix Sparse and low-rank estimator Estimation rate Alternating direction method of multipliers 
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