Related papers: Bounding Distance Between Outputs in Distributed L…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
In this paper, we present distributed fault-tolerant algorithms that approximate the centroid (i.e., the average) of a set of $n$ data points in $\mathbb{R}^d$. Our work falls into the broader area of multidimensional Byzantine approximate…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
Consider the stationary measure of open asymmetric simple exclusion process (ASEP) on the lattice $\{1,\dots,n\}$. Taking $n$ to infinity while fixing the jump rates, this measure converges to a measure on the semi-infinite lattice. In the…
Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…
This paper addresses the quantitative verification of finite-time constrained occupation time for stochastic continuous-time systems governed by stochastic differential equations (SDEs). Unlike classical reachability analysis, which focuses…
This paper is devoted to studying the stationary solutions of a general constrained optimization problem through its associated unconstrained penalized problems. We aim to answer the question, "what do the stationary solutions of a…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
In this paper we study a multi-robot path planning problem for persistent monitoring of an environment. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum time…