Related papers: Network Flows that Solve Sylvester Matrix Equation…
In this paper, an iterative algorithm is presented for solving Sylvester tensor equation $\mathscr{A}*_M\mathscr{X}+\mathscr{X}*_N\mathscr{C}=\mathscr{D}$, where $\mathscr{A}$, $\mathscr{C}$ and $\mathscr{D}$ are given tensors with…
This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas,…
In this paper we consider a network with $P$ nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^\star$ minimizing the sum of all…
This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
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…
In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…
In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form $Ax = b$ assuming that the equation has at least one solution. The equation is presumed to be solved by $m$ agents assuming that each…
A distributed discrete-time algorithm is proposed for multi-agent networks to achieve a common least squares solution of a group of linear equations, in which each agent only knows some of the equations and is only able to receive…
This paper proposes a double-layered framework (or form of network) to integrate two mechanisms, termed consensus and conservation, achieving distributed solution of a linear equation. The multi-agent framework considered in the paper is…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this paper, a class of convex feasibility problems (CFPs) are studied for multi-agent systems through local interactions. The objective is to search a feasible solution to the convex inequalities with some set constraints in a…
We consider Newton methods for common types of single commodity and multi-commodity network flow problems. Despite the potentially very large dimension of the problem, they can be implemented using the conjugate gradient method and…
We use queueing networks to present a new approach to solving Laplacian systems. This marks a significant departure from the existing techniques, mostly based on graph-theoretic constructions and sampling. Our distributed solver works for a…
As the complexity of our neural network models grow, so too do the data and computation requirements for successful training. One proposed solution to this problem is training on a distributed network of computational devices, thus…
Distributed model predictive control (MPC) has been proven a successful method in regulating the operation of large-scale networks of constrained dynamical systems. This paper is concerned with cooperative distributed MPC in which the…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…