Related papers: Network Flows that Solve Sylvester Matrix Equation…
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…
In the purpose of making the consensus algorithm robust to outliers, consensus on the median value has recently attracted some attention. It has its applicability in for instance constructing a resilient distributed state estimator.…
Distributed computing is a standard way to scale up machine learning and data science algorithms to process large amounts of data. In such settings, avoiding communication amongst machines is paramount for achieving high performance. Rather…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
We present a distributed asynchronous algorithm for approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is a positive definite real matrix, and $b \in \mathbb{R}^n$. This is equivalent to…
We consider the convolution equation $F*X=B$, where $F\in\mathbb{R}^{3\times 3}$ and $B\in\mathbb{R}^{m\times n}$ are given, and $X\in\mathbb{R}^{m\times n}$ is to be determined. The convolution equation can be regarded as a linear system…
Distributed resource allocation is a central task in network systems such as smart grids, water distribution networks, and urban transportation systems. When solving such problems in practice it is often important to have nonasymptotic…
This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques…
We present our public-domain software for the following tasks in sparse (or toric) elimination theory, given a well-constrained polynomial system. First, C code for computing the mixed volume of the system. Second, Maple code for defining…
The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction. The few available…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
In this paper, we study the distributed optimization problem for a system of agents embedded in time-varying directed communication networks. Each agent has its own cost function and agents cooperate to determine the global decision that…
Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically…
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…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…