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[期刊论文]

QUADRATIC GROWTH CONDITIONS FOR CONVEX MATRIX OPTIMIZATION PROBLEMS ASSOCIATED WITH SPECTRAL FUNCTIONS

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Author:

Cui, Ying (Cui, Ying.) | Ding, Chao (Ding, Chao.) | Zhao, Xinyuan (Zhao, Xinyuan.) (Scholars:赵欣苑)

Indexed by:

EI Scopus SCIE

Abstract:

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 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.

Keyword:

quadratic growth conditions matrix optimization metric sub regularity spectral functions augmented Lagrangian function fast convergence rates

Author Community:

  • [ 1 ] [Cui, Ying]Natl Univ Singapore, Dept Math, Singapore, Singapore
  • [ 2 ] [Ding, Chao]Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing, Peoples R China
  • [ 3 ] [Zhao, Xinyuan]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing, Peoples R China

Reprint Author's Address:

  • [Cui, Ying]Natl Univ Singapore, Dept Math, Singapore, Singapore

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Source :

SIAM JOURNAL ON OPTIMIZATION

ISSN: 1052-6234

Year: 2017

Issue: 4

Volume: 27

Page: 2332-2355

3 . 1 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:66

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 16

SCOPUS Cited Count: 15

30 Days PV: 3

Affiliated Colleges:

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