Related papers: On the Connection between Dynamical Optimal Transp…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has…
We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
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…