Related papers: Convergence of the Sinkhorn algorithm when the Sch…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and…
In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian…
This note is devoted to the study of the finite volume methods used in the discretization of degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The notion of an entropy-process solution, successfully used for the…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
Recently, Sinkhorn's algorithm was applied for approximately solving linear programs emerging from optimal transport very efficiently. This was accomplished by formulating a regularized version of the linear program as Bregman projection…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…
We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element…
We develop a quantitative contraction framework for Schrodinger and Sinkhorn bridges based on transportation-cost inequalities and Riccati matrix difference equations. Our approach combines logarithmic Sobolev and Talagrand-type…
We introduce and prove convergence of a damped Newton algorithm to approximate solutions of the semi-discrete optimal transport problem with storage fees, corresponding to a problem with hard capacity constraints. This is a variant of the…
We propose accelerated versions of the operator Sinkhorn iteration for operator scaling using successive overrelaxation. We analyze the local convergence rates of these accelerated methods via linearization, which allows us to determine the…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
We propose and study a system of Schr\"odinger's problems and functional equations in probability theory. More precisely, we consider a system of variational problems of relative entropies for probability measures on a Euclidean space with…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
The Schr\"{o}dinger Bridge Problem (SBP), which can be understood as an entropy-regularized optimal transport, seeks to compute stochastic dynamic mappings connecting two given distributions. SBP has shown significant theoretical importance…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…