Related papers: Efficient Computing Algorithm for High Dimensional…
This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…
Data characterized by high dimensionality and sparsity are commonly used to describe real-world node interactions. Low-rank representation (LR) can map high-dimensional sparse (HDS) data to low-dimensional feature spaces and infer node…
This work presents a new method for online selection of multiple penalty parameters for the alternating direction method of multipliers (ADMM) algorithm applied to optimization problems with multiple constraints or functionals with block…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
The time complexity of support vector machines (SVMs) prohibits training on huge data sets with millions of data points. Recently, multilevel approaches to train SVMs have been developed to allow for time-efficient training on huge data…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate…
All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…
In this paper, we propose an alternating direction method of multipliers (ADMM)-based optimization algorithm to achieve better undersampling rate for multiple measurement vector (MMV) problem. The core is to introduce the $\ell_{2,0}$-norm…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known…
In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
In this paper, we review the parallel and distributed optimization algorithms based on the alternating direction method of multipliers (ADMM) for solving "big data" optimization problems in modern communication networks. We first introduce…
This paper considers the distributed optimization of a sum of locally observable, non-convex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
This paper presents approaches to compute sparse solutions of Generalized Singular Value Problem (GSVP). The GSVP is regularized by $\ell_1$-norm and $\ell_q$-penalty for $0<q<1$, resulting in the $\ell_1$-GSVP and $\ell_q$-GSVP…
In recent years, several convergent multi-block variants of the alternating direction method of multipliers (ADMM) have been proposed for solving the convex quadratic semidefinite programming via its dual, which is naturally a 3-block…
Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…