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We study the Monge and Kantorovich transportation problems on $\mathbb{R}^{\infty}$ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal…
We study random multidimensional assignment problems where the costs decompose into the sum of independent random variables. In particular, in three dimensions, we assume that the costs $W_{i,j,k}$ satisfy…
We give a sufficient and necessary condition for a probability measure $\mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and…
Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected…
It is well-known that duality in the Monge-Kantorovich transport problem holds true provided that the cost function $c:X\times Y\to [0,\infty]$ is lower semi-continuous or finitely valued, but it may fail otherwise. We present a suitable…
We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to…
We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d $\ge$ 3 dimensions, where the matching cost between two points is given by any…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
We show that the average cost for the traveling-salesman problem in two dimensions, which is the archetypal problem in combinatorial optimization, in the bipartite case, is simply related to the average cost of the assignment problem with…
This paper deals with the existence of optimal transport maps for some optimal transport problems with a convex but non strictly convex cost. We give a decomposition strategy to address this issue. As part of our strategy, we have to treat…
We investigate the convergence rate of the optimal entropic cost $v_\varepsilon$ to the optimal transport cost as the noise parameter $\varepsilon \downarrow 0$. We show that for a large class of cost functions $c$ on $\mathbb{R}^d\times…
Constrained Markov decision processes (CMDPs) are used as a decision-making framework to study the long-run performance of a stochastic system. It is well-known that a stationary optimal policy of a CMDP problem under discounted cost…
We study a multi-marginal optimal transportation problem with a cost function of the form $c(x_{1}, \ldots,x_{m})=\sum_{k=1}^{m-1}|x_{k}-x_{k+1}|^{2} + |x_{m}- F(x_{1})|^{2}$, where $F: \mathbb{R}^n \rightarrow \mathbb{R}^n$. When $m=4$,…
We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration…
We consider the Monge-Kantorovich problem between two random measuress. More precisely, given probability measures $\mathbb{P}_1,\mathbb{P}_2\in\mathcal{P}(\mathcal{P}(M))$ on the space $\mathcal{P}(M)$ of probability measures on a smooth…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using…
In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the…
We prove that if $\Omega\subset \mathbb{R}^{n+1}$ is a (not necessarily strictly) convex, $C^1$ domain, and $\mu$ and $\bar{\mu}$ are probability measures absolutely continuous with respect to surface measure on $\partial \Omega$, with…