Related papers: Aug-PDG: Linear Convergence of Convex Optimization…
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
We show that the augmented primal-dual gradient algorithms can achieve global exponential convergence with partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a…
This work studies a class of non-smooth decentralized multi-agent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common non-smooth term. We propose a general primal-dual…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…