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We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive…
Decentralized distributed optimization over time-varying graphs (networks) is nowadays a very popular branch of research in optimization theory and consensus theory. One of the motivations to consider such networks is an application to…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
This paper studies Dictionary Learning problems wherein the learning task is distributed over a multi-agent network, modeled as a time-varying directed graph. This formulation is relevant, for instance, in Big Data scenarios where massive…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem.…
Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of…
We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A…
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,…
This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization problem, in which both distributed agents and a central coordinator contribute independent, potentially conflicting…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet.…
This paper studies decentralized stochastic nonconvex optimization problem over row-stochastic networks. We consider the heavy-tailed gradient noise which is empirically observed in many popular real-world applications. Specifically, we…
We consider the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph. Motivated by target tracking and parameter estimation problems in intermittently connected robotic and sensor networks, the…