A Modified Proximal Symmetric ADMM for Multi-Block Separable Convex Optimization with Linear Constraints

We consider the linearly constrained separable convex optimization problem whose objective function is separable w.r.t. $m$ blocks of variables. A bunch of methods have been proposed and well studied. Specifically, a modified strictly contractive Peaceman-Rachford splitting method (SC-PRCM) has been well studied in the literature for the special case of $m=3$. Based on the modified … Read more

A Partial PPa S-ADMM for Multi-Block for Separable Convex Optimization with Linear Constraints

The symmetric alternating direction method of multipliers (S-ADMM) is a classical effective method for solving two-block separable convex optimization. However, its convergence may not be guaranteed for multi-block case providing there is no additional assumptions. In this paper, we propose a partial PPa S-ADMM (referred as P3SADMM), which updates the Lagrange multiplier twice with suitable … Read more

A New Sequential Updating Scheme of the Lagrange Multiplier for Multi-Block Linearly Constrained Separable Convex Optimization with Relaxed Step Sizes

In various applications such as signal/image processing, data mining, statistical learning and etc., the multi-block linearly constrained separable convex optimization is frequently used, where the objective function is the sum of multiple individual convex functions, and the major constraints are linear. A classical method for solving such kind of optimization problem could be the alternating … Read more

A Partial PPA block-wise ADMM for Multi-Block Constrained Separable Convex Optimization

The alternating direction method of multipliers(ADMM) has been proved to be effective for solving two-block separable convex optimization subject to linear constraints. However, it is not necessarily convergent when it is extended to multiple-block case directly. One remedy could be regrouping multiple-block variables into two groups firstly and then adopting the classic ADMM to the … Read more

An Alternating Minimization Method for Matrix Completion Problem

In this paper, we focus on solving matrix completion problem arising from applications in the fields of information theory, statistics, engineering, etc. However, the matrix completion problem involves nonconvex rank constraints which make this type of problem difficult to handle. Traditional approaches use a nuclear norm surrogate to replace the rank constraints. The relaxed model … Read more

Constraints reduction programming by subset selection: a study from numerical aspect

We consider a novel method entitled constraints reduction programming which aims to reduce the constraints in an optimization model. This method is derived from various applications of management or decision making, and has potential ability to handle a wider range of applications. Due to the high combinatorial complexity of underlying model, it is difficult to … Read more

An Alternating Minimization Method for Robust Principal Component Analysis

We focus on solving robust principal component analysis (RPCA) arising from various applications such as information theory, statistics, engineering, and etc. We adopt a model to minimize the sum of observation error and sparsity measurement subject to the rank constraint. To solve this problem, we propose a two-step alternating minimization method. In one step, a … Read more

Partial Convolution for Total Variation Deblurring and Denoising by New Linearized Alternating Direction Method of Multipliers with Extension Step

In this paper, we propose a partial convolution model for image delburring and denoising. We also devise a new linearized alternating direction method of multipliers (ADMM) with extension step. On one hand, the computation of its subproblem is dominated by several FFTs, hence its per-iteration cost is low, on the other hand, the relaxed parameter … Read more