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Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems
(2010-08)
A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all ...
An Alternating Direction and Projection Algorithm for Structure-enforced Matrix Factorization
(2013-10)
Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models ap- pearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning ...
Augmented Lagrangian Alternating Direction Method for Matrix Separation Based on Low-Rank Factorization
(2011-01)
The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. ...
An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors
(2011-01)
This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to nd nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates ...
A Compressive Sensing and Unmixing Scheme for Hyperspectral Data Processing
(2011-01)
Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation and I/O throughputs, especially when real-time processing is desired. In this paper, we investigate a ...
Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation
(2015-06)
Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts ...
An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization
(2012-07)
Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) ...
Trace-Penalty Minimization for Large-scale Eigenspace Computation
(2013-02)
The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high-dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be ...
Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions
(2012-03)
In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations ...
Group Sparse Optimization by Alternating Direction Method
(2011-04)
This paper proposes efficient algorithms for group sparse optimization with mixed L21-regularization, which arises from the reconstruction of group sparse signals in compressive sensing, and the group Lasso problem in ...