Related papers: Alternating Direction Method of Multipliers for Sp…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…
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…
This paper studies a proximal alternating direction method of multipliers (ADMM) with variable metric indefinite proximal terms for linearly constrained convex optimization problems. The proximal ADMM plays an important role in many…
In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the…
It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…
We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
Model Predictive Control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC this constraint is generally taken on a polyhedral set, leading to a quadratic…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…
In this paper, we aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this,…
We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…
The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial…
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…