相关论文: Convergence of the Sinkhorn algorithm when the Sch…

The aim of this article is to show that the Monge-Kantorovich problem is the limit of a sequence of entropy minimization problems when a fluctuation parameter tends down to zero. We prove the convergence of the entropic values to the…

\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…

The Schr\"odinger bridge problem (SBP) is gaining increasing attention in generative modeling and showing promising potential even in comparison with the score-based generative models (SGMs). SBP can be interpreted as an entropy-regularized…

Solutions to the Schr\"{o}dinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute the same, the dynamic Sinkhorn recursion has become a…

This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…

This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient…

Starting from Brenier's relaxed formulation of the incompressible Euler equation in terms of geodesics in the group of measure-preserving diffeomorphisms, we propose a numerical method based on Sinkhorn's algorithm for the entropic…

A recent breakthrough in Edmonds' problem showed that the noncommutative rank can be computed in deterministic polynomial time, and various algorithms for it were devised. However, only quite complicated algorithms are known for finding a…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

We propose a scalable approximate algorithm for the NP-hard maximum-weight independent set problem. The core component of our algorithm is a dual coordinate descent applied to a smoothed LP relaxation of the problem. This technique is…

We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…

We pose the problem of approximating optimally a given nonnegative signal with the scalar autoconvolution of a nonnegative signal. The I-divergence is chosen as the optimality criterion being well suited to incorporate nonnegativity…

We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact subsets of Euclidean space. We consider the case of…

We pose the problem of the optimal approximation of a given nonnegative signal $y_t$ with the scalar autoconvolution $(x*x)_t$ of a nonnegative signal $x_t$, where $x_t$ and $y_t$ are signals of equal length. The $\mathcal{I}$-divergence…

We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…

In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…

In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and…

Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…

The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…