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Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains,…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
This paper addresses the problem of resource allocation for systems in which a primary and a secondary link share the available spectrum by an underlay or overlay approach. After observing that such a scenario models both cognitive radio…
The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations.…
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
Distributed stochastic non-convex optimization problems have recently received attention due to the growing interest of signal processing, computer vision, and natural language processing communities in applications deployed over…
Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…
We propose an algorithm for distributed optimization over time-varying communication networks. Our algorithm uses an optimized ratio between the number of rounds of communication and gradient evaluations to achieve fast convergence. The…
This paper proposes a novel family of primal-dual-based distributed algorithms for smooth, convex, multi-agent optimization over networks that uses only gradient information and gossip communications. The algorithms can also employ…
We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the…
We consider stochastic optimization with delayed gradients where, at each time step $t$, the algorithm makes an update using a stale stochastic gradient from step $t - d_t$ for some arbitrary delay $d_t$. This setting abstracts asynchronous…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
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 investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a…
The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…
In this paper, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the…