Related papers: Notes on the primal-dual algorithm for convex opti…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

In this paper, we propose the primal-dual method of multipliers (PDMM) for distributed optimization over a graph. In particular, we optimize a sum of convex functions defined over a graph, where every edge in the graph carries a linear…

We provide a general method to convert a "primal" black-box algorithm for solving regularized convex-concave minimax optimization problems into an algorithm for solving the associated dual maximin optimization problem. Our method adds…

A new method for reducing metal artifacts in X-ray computed tomography (CT) images is presented. It bases on the solution of a convex optimization problem with inequality constraints on the sinogram, and total variation regularization for…

We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…

This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…

We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…

Digital breast tomosynthesis is rapidly replacing digital mammography as the basic x-ray technique for evaluation of the breasts. However, the sparse sampling and limited angular range gives rise to different artifacts, which manufacturers…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…

This paper deals with the analysis of a recent reformulation of the primal-dual hybrid gradient method [Zhu and Chan 2008, Pock, Cremers, Bischof and Chambolle 2009, Esser, Zhang and Chan 2010, Chambolle and Pock 2011], which allows to…

The Learned Primal Dual (LPD) method has shown promising results in various tomographic reconstruction modalities, particularly under challenging acquisition restrictions such as limited viewing angles or a limited number of views. We…

We consider algorithms for solving structured convex optimization problems over a network of agents with communication delays. It is assumed that each agent performs its local updates by using possibly outdated information from its…

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex…