Built on

R.M. Larsen
1998
Earlier work this paper cites.
L. Li, W. Huang, I. Gu, and Q. Tian
2004
Earlier work this paper cites.
Y. Nesterov
2004
Earlier work this paper cites.
P. Tseng
2008
Earlier work this paper cites.

Similar

A. Beck and M. Teboulle
2009
Cited alongside, same era.
Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, and Y. Ma
2009
Cited alongside, same era.
J. Wright, A. Ganesh, S. Rao, Y. Peng, and Y. Ma
2009
Cited alongside, same era.
arXiv:0912.4571v2, October 2010
Original
D. Goldfarb, S. Ma, and K. Scheinberg · 2010
Cited alongside, same era.

Then

Z. Zhou, X. Li, J. Wright, E. Candès, and Y. Ma
Original
2010
Later among the works it cites.
E. J. Candès, X. Li, Y. Ma, and Wright J
2011
Closest in time.
Z. Lin, M. Chen, L. Wu, and Y. Ma
Original
2011
Closest in time.
M. Tao and X. Yuan
2011
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2011

Fast First-Order Methods for Stable Principal Component Pursuit

Aybat, Necdet Serhat, Goldfarb, Donald, Iyengar, Garud

Understand

The stable principal component pursuit (SPCP) problem is a non-smooth convex optimization problem, the solution of which has been shown both in theory and in practice to enable one to recover the low rank and sparse components of a matrix whose elements have been corrupted by Gaussian noise.

In this paper, we show how several fast first-order methods can be applied to this problem very efficiently.
Specifically, we show that the subproblems that arise when applying optimal gradient methods of Nesterov, alternating linearization methods and alternating direction augmented Lagrangian methods to the SPCP problem either have closed-form solutions or have solutions that can be obtained with very modest effort.
All but one of the methods analyzed require at least one of the non-smooth terms in the objective function to be smoothed and obtain an eps-optimal solution to the SPCP problem in O(1/eps) iterations.