A Relax Inexact Accelerated Proximal Gradient Method for the Constrained Minimization Problem of Maximum Eigenvalue Functions
Joint Authors
Wang, Wei
Li, Shanghua
Gao, Jingjing
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-09
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
For constrained minimization problem of maximum eigenvalue functions, since the objective function is nonsmooth, we can use the approximate inexact accelerated proximal gradient (AIAPG) method (Wang et al., 2013) to solve its smooth approximation minimization problem.
When we take the function g(X)=δΩ(X) (Ω∶={X∈Sn:F(X)=b,X⪰0}) in the problem min{λmax(X)+g(X):X∈Sn}, where λmax(X) is the maximum eigenvalue function, g(X) is a proper lower semicontinuous convex function (possibly nonsmooth) and δΩ(X) denotes the indicator function.
But the approximate minimizer generated by AIAPG method must be contained in Ω otherwise the method will be invalid.
In this paper, we will consider the case where the approximate minimizer cannot be guaranteed in Ω.
Thus we will propose two different strategies, respectively, constructing the feasible solution and designing a new method named relax inexact accelerated proximal gradient (RIAPG) method.
It is worth mentioning that one advantage when compared to the former is that the latter strategy can overcome the drawback.
The drawback is that the required conditions are too strict.
Furthermore, the RIAPG method inherits the global iteration complexity and attractive computational advantage of AIAPG method.
American Psychological Association (APA)
Wang, Wei& Li, Shanghua& Gao, Jingjing. 2014. A Relax Inexact Accelerated Proximal Gradient Method for the Constrained Minimization Problem of Maximum Eigenvalue Functions. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-495677
Modern Language Association (MLA)
Wang, Wei…[et al.]. A Relax Inexact Accelerated Proximal Gradient Method for the Constrained Minimization Problem of Maximum Eigenvalue Functions. Journal of Applied Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-495677
American Medical Association (AMA)
Wang, Wei& Li, Shanghua& Gao, Jingjing. A Relax Inexact Accelerated Proximal Gradient Method for the Constrained Minimization Problem of Maximum Eigenvalue Functions. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-495677
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-495677