Related papers: First-order primal-dual algorithm with correction
In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly…
We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…
We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates…
Saddle-point or primal-dual methods have recently attracted renewed interest as a systematic technique to design distributed algorithms which solve convex optimization problems. When implemented online for streaming data or as dynamic…
The primal-dual algorithm recently proposed by Chambolle & Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle & Pock in \cite{CP11} and also by Shefi & Teboulle in…
In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix $D$. Relaxing requirement on…
In this paper, we propose a new primal-dual algorithm for minimizing $f(x) + g(x) + h(Ax)$, where $f$, $g$, and $h$ are proper lower semi-continuous convex functions, $f$ is differentiable with a Lipschitz continuous gradient, and $A$ is a…
We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
In this work we consider a possibility to use the conception of $(\delta, L)$-model of a function for optimization tasks, whereby solving a primal problem there is a necessity to recover a solution of a dual problem. The conception of…
In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
In this paper, we consider first-order convergence theory and algorithms for solving a class of non-convex non-concave min-max saddle-point problems, whose objective function is weakly convex in the variables of minimization and weakly…