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We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
The paper addresses a sequential changepoint detection problem, assuming that the duration of change may be finite and unknown. This problem is of importance for many applications, e.g., for signal and image processing where signals appear…
We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require $O(\log_2\log_2 n)$ queries on average…
Congestion pricing has become an effective instrument for traffic demand management on road networks. This paper proposes an optimal control approach for congestion pricing for day-to-day timescale that incorporates demand uncertainty and…
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the discount factor $\lambda$ tends to zero. In the literature,…
Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor…
The paper studies the expectation of the inspection time in complex aging systems. Under reasonable assumptions, this problem is reduced to studying the expectation of the length of the shortest path in the directed degradation graph of the…
This paper is an extension of Part I of a series about Nu-class multifunctions. A method is presented for computing the integrated mean-squared prediction error (IMSPE) in the design of computer experiments, when the prediction domain is a…
We consider a discrete version of the Witsenhausen problem where all random variables are bounded and take on integer values. Our main goal is to understand the complexity of computing good strategies given the distributions for the initial…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…
We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
In this paper, we consider the problem of choosing disks (that we can think of as corresponding to wireless sensors) so that given a set of input points in the plane, there exists no path between any pair of these points that is not…
While dynamic policies have historically formed the foundation of most influential papers dedicated to the joint replenishment problem, we are still facing profound gaps in our structural understanding of optimal such policies as well as in…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
In the present work, we study the optimal control paths in the Zermelo navigation problem from the geometric and differential equations point of view rather than the optimal control point of view, where the latter has been carried out in…
For a set $P$ of $n$ points in the plane and a value $r > 0$, the unit-disk range reporting problem is to construct a data structure so that given any query disk of radius $r$, all points of $P$ in the disk can be reported efficiently. We…
It is very well known that when the exact line search gradient descent method is applied to a convex quadratic objective, the worst-case rate of convergence (ROC), among all seed vectors, deteriorates as the condition number of the Hessian…
The failure diagnosis for {\it discrete event systems} (DESs) has been given considerable attention in recent years. Both on-line and off-line diagnostics in the framework of DESs was first considered by Lin Feng in 1994, and particularly…