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The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion,…
In this paper, we present the first constant-approximation algorithm for {\em budgeted sweep coverage problem} (BSC). The BSC involves designing routes for a number of mobile sensors (a.k.a. robots) to periodically collect information as…
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic…
We push the limit in planning collision-free motions for routing uniform labeled discs in two dimensions. First, from a theoretical perspective, we show that the constant-factor time-optimal routing of labeled discs can be achieved using a…
This paper studies an optimal control problem for a string of vehicles with safety requirements and finite-time specifications on the approach time to a target region. Our problem formulation is motivated by scenarios involving autonomous…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
A simple procedure to map two probability measures in $\mathbb{R}^d$ is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
Let $D$ be a directed graph cellularly embedded in a surface together with non-negative cost on its arcs. Given any integer circulation in $D$, we study the problem of finding a minimum-cost non-negative integer circulation in $D$ that is…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
The anticipated launch of fully autonomous vehicles presents an opportunity to develop and implement novel traffic management systems. Intersections are one of the bottlenecks for urban traffic, and thus offer tremendous potential for…
This paper studies optimal time-bounded control in multi-mode systems with discrete costs. Multi-mode systems are an important subclass of linear hybrid systems, in which there are no guards on transitions and all invariants are global.…
A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an aggregative term in the cost function. The problems are…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer…
Nonlinear stabilization using control contraction metric (CCM) method usually involves an online optimization problem to compute a minimal geodesic (a shortest path) between pair of states, which is not desirable for real-time applications.…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…