Related papers: Time Parameterized Optimal Transport
Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…
Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…
This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with…
The subpath planning problem is a branch of the path planning problem, which has widespread applications in automated manufacturing process as well as vehicle and robot navigation. This problem is to find the shortest path or tour subject…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…
We study optimal transport between two high-dimensional distributions $\mu,\nu$ in $R^n$ from an algorithmic perspective: given $x \sim \mu$, find a close $y \sim \nu$ in $poly(n)$ time, where $n$ is the dimension of $x,y$. Thus, running…
The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
Modern applied optimization problems become more and more complex every day. Due to this fact, distributed algorithms that can speed up the process of solving an optimization problem through parallelization are of great importance. The main…
We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
The ridesharing problem is that given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to…
In this paper we address several constrained transportation optimization problems (e.g. vehicle routing, shortest Hamiltonian path), for which we present novel algorithmic solutions and extensions, considering several optimization…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
Real-world problems are very difficult to optimize. However, many researchers have been solving benchmark problems that have been extensively investigated for the last decades even if they have very few direct applications. The Traveling…
Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed…
This paper presents a robust and efficient method for tracking topological features in time-varying scalar data. Structures are tracked based on the optimal matching between persistence diagrams with respect to the Wasserstein metric. This…
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the $L^2$-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on graph (lattice) with different…