相关论文: On starting and stopping criteria for nested prima…

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…

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 is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

Non-convex optimization problems are challenging to solve; the success and computational expense of a gradient descent algorithm or variant depend heavily on the initialization strategy. Often, either random initialization is used or…

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…

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 two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…

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…

We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…

We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…

In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…

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…