Related papers: An Alternating Direction Method for Finding Dantzi…

Recently, semidefinite programming performance estimation has been employed as a strong tool for the worst-case performance analysis of first order methods. In this paper, we derive new non-ergodic convergence rates for the alternating…

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…

Multi-way data arises in many applications such as electroencephalography (EEG) classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit…

In the late sixties, N. Shor and B. Polyak independently proposed optimal first-order methods for non-smooth convex optimization problems. In 1982 A. Nemirovski proposed optimal first-order methods for smooth convex optimization problems,…

Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex…

In this work, we adopt Wyner common information framework for unsupervised multi-view representation learning. Within this framework, we propose two novel formulations that enable the development of computational efficient solvers based on…

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…

Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital…

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. A new class of random asynchronous distributed optimization methods is introduced. The methods…

We present here a new method for evaluating determinants -- the reduction method. Firstly, in the section 2, we apply it to third-order determinants and after, in the section 3, we generalize it to higher-order determinants. In the section…

By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…

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 exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…