Related papers: Decentralized gradient algorithm for solution of a…
We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
This paper studies decentralized optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which is…
Solving a large-scale system of linear equations is a key step at the heart of many algorithms in machine learning, scientific computing, and beyond. When the problem dimension is large, computational and/or memory constraints make it…
A version of the Dynamical Systems Method (DSM) for solving ill-conditioned linear algebraic systems is studied in this paper. An {\it a priori} and {\it a posteriori} stopping rules are justified. An algorithm for computing the solution…
In this paper, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
Decentralized learning over distributed datasets can have significantly different data distributions across the agents. The current state-of-the-art decentralized algorithms mostly assume the data distributions to be Independent and…
We propose a novel stochastic gradient descent method for solving linear least squares problems with partially observed data. Our method uses submatrices indexed by a randomly selected pair of row and column index sets to update the iterate…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning…
This paper investigates the problem of solving discrete-time Lyapunov equations (DTLE) over a multi-agent system, where every agent has access to its local information and communicates with its neighbors. To obtain a solution to DTLE, a…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…
In this paper, we study distributed methods for solving a Sylvester equation in the form of AX+XB=C for matrices A, B, C$\in R^{n\times n}$ with X being the unknown variable. The entries of A, B and C (called data) are partitioned into a…
In multi-agent reinforcement learning (MARL), it is challenging for a collection of agents to learn complex temporally extended tasks. The difficulties lie in computational complexity and how to learn the high-level ideas behind reward…
We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…
This paper proposes a new architecture for multi-agent systems to cover an unknowingly distributed fast, safely, and decentralizedly. The inter-agent communication is organized by a directed graph with fixed topology, and we model agent…