相关论文: Two Stage Algorithm for Semi-Discrete Optimal Tran…

We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…

We develop a semi-discrete optimal transport scheme for the compressible semi-geostrophic equations, a system that plays an important role in modelling large-scale atmospheric dynamics and frontogenesis. Unlike the incompressible case, the…

Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…

We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…

We compute exact second-order asymptotics for the cost of an optimal solution to the entropic optimal transport problem in the continuous-to-discrete, or semi-discrete, setting. In contrast to the discrete-discrete or continuous-continuous…

We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…

Semi-discrete transport can be characterized in terms of real-valued shifts. Often, but not always, the solution to the shift-characterized problem partitions the continuous region. This paper gives examples of when partitioning fails, and…

This paper deals with the 3/4-discrete 2-Wasserstein optimal transport between two measures, where one is supported by a set of segment and the other one is supported by a set of Dirac masses. We select the most suitable optimization…

We propose and analyze a modified damped Newton algorithm to solve the semi-discrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each…

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…

We show that the discrete Sinkhorn algorithm - as applied in the setting of Optimal Transport on a compact manifold - converges to the solution of a fully non-linear parabolic PDE of Monge-Ampere type, in a large-scale limit. The latter…

We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…

We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex…

We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier…

Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In…

In this paper, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate the problem using direct optimal control and exploit the structure to construct a semi-distributed…

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…