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Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…
This paper focuses on a distributed coupled constrained convex optimization problem over directed unbalanced and time-varying multi-agent networks, where the global objective function is the sum of all agents' private local objective…
This paper develops a distributed primal-dual algorithm via event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some…
We generalize the well-known primal-dual algorithm proposed by Chambolle and Pock for saddle point problems, and improve the condition for ensuring its convergence. The improved convergence-guaranteeing condition is effective for the…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…
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…
This paper investigates the distributed online optimization problem over a multi-agent network subject to local set constraints and coupled inequality constraints, which has a lot of applications in many areas, such as wireless sensor…
We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which…
The saddle-point problems (SPPs) with nonlinear coupling operators frequently arise in various control systems, such as dynamic programming optimization, H-infinity control, and Lyapunov stability analysis. However, traditional primal-dual…
Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean…
In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in…
Saddle point problems arise from many wireless applications, and primal-dual iterative algorithms are widely applied to find the saddle points. In the existing literature, the convergence results of such algorithms are established assuming…