Related papers: On the improved conditions for some primal-dual al…

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly…

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a…

Consideration of the primal and dual problems together leads to important new insights into the characteristics of boosting algorithms. In this work, we propose a general framework that can be used to design new boosting algorithms. A wide…

Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…

Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…

We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation model, can be written in terms of generalized conjugates of convex…

In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…

We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…

The note contains a direct extension of the Chambolle and Pock convergence proof of the primal-dual hybrid gradient (PDHG) algorithm to the case of monotone inclusions.

Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…

Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm,…

The paper presents primal-dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat-Vu…

Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with…