Shiqian Ma

Publications
Influence

Fixed point and Bregman iterative methods for matrix rank minimization

Shiqian Ma, D. Goldfarb, L. Chen
Computer Science, Mathematics
Math. Program.
11 May 2009

We propose fixed point and Bregman iterative algorithms for solving the nuclear norm minimization problem and prove convergence of the first of these algorithms. Expand

An efficient algorithm for compressed MR imaging using total variation and wavelets

Shiqian Ma, Wotao Yin, Yin Zhang, Amit Chakraborty
Mathematics, Computer Science
IEEE Conference on Computer Vision and Pattern…
23 June 2008

Compressed sensing, an emerging multidisciplinary field involving mathematics, probability, optimization, and signal processing, focuses on reconstructing an unknown signal from a very limited number of samples. Expand

Fast alternating linearization methods for minimizing the sum of two convex functions

D. Goldfarb, Shiqian Ma, K. Scheinberg
Computer Science, Mathematics
Math. Program.
23 December 2009

We present in this paper alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions, with little change in the computational effort required at each iteration. Expand

Sparse Inverse Covariance Selection via Alternating Linearization Methods

K. Scheinberg, Shiqian Ma, D. Goldfarb
Mathematics, Computer Science
NIPS
30 October 2010

Gaussian graphical models are of great interest in statistical learning. Expand

Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization

D. Goldfarb, Shiqian Ma
Mathematics, Computer Science
Found. Comput. Math.
18 June 2009

In this paper, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Expand

Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

Xiao Wang, Shiqian Ma, D. Goldfarb, W. Liu
Mathematics, Computer Science
SIAM J. Optim.
3 December 2014

We propose a general framework of stochastic quasi-Newton methods for solving nonconvex optimization, where we assume that only stochastically information of the gradients of the objective function is available via a first-order oracle (SFO). Expand

Barzilai-Borwein Step Size for Stochastic Gradient Descent

Conghui Tan, Shiqian Ma, Y. Dai, Yuqiu Qian
Mathematics, Computer Science
NIPS
13 May 2016

We propose to use the Barzilai-Borwein method to automatically compute step sizes for SGD and its variant: stochastic variance reduced gradient (SVRG) method, which leads to two algorithms: SGD-BB and SVRG-BB. Expand

Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection

Shiqian Ma, Lingzhou Xue, H. Zou
Computer Science, Mathematics
Neural Computation
6 June 2012

In this letter, we propose two alternating direction methods for solving the convex optimization problem for graphical model selection in the presence of unobserved variables. Expand

On the Global Linear Convergence of the ADMM with MultiBlock Variables

Tianyi Lin, Shiqian Ma, S. Zhang
Mathematics, Computer Science
SIAM J. Optim.
19 August 2014

We show that under some easily verifiable and reasonable conditions the global linear convergence of the alternating direction method of multipliers can still be ensured, which is important since the ADMM is a popular method for solving large-scale multiblock optimization models and is known to perform very well in practice even when $N\ge 3$. Expand

Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis

B. Jiang, Tianyi Lin, Shiqian Ma, S. Zhang
Mathematics, Computer Science
Comput. Optim. Appl.
9 May 2016

This paper aims to take one step in the direction of disciplined nonconvex and nonsmooth optimization, using proximal-type variants of the ADMM to solve such a model, assuming the proximal ADMM updates can be implemented for all the block variables. Expand

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