Related papers: Fast iterative solvers for an optimal transport pr…
An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
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…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial…
This paper provides a theoretical and numerical approach to show existence, uniqueness, and the numerical determination of metalenses refracting radiation with energy patterns. The theoretical part uses ideas from optimal transport and for…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…
This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arrive at continuous norms that enable analysis of well-posedness…