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Laue tomography experiments retrieve the positions and orientations of crystal grains in a polycrystalline samples from diffraction patterns recorded at multiple viewing angles. The use of a broad wavelength spectrum beam can greatly reduce…

Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…

Optimization and Control · Mathematics 2025-02-13 Tianhao Wu , Qihao Cheng , Zihao Wang , Chaorui Zhang , Bo Bai , Zhongyi Huang , Hao Wu

We present a registration method for model reduction of parametric partial differential equations with dominating advection effects and moving features. Registration refers to the use of a parameter-dependent mapping to make the set of…

Numerical Analysis · Mathematics 2023-09-28 Tobias Blickhan

A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…

Computation · Statistics 2025-11-11 Zichu Wang , Esteban G. Tabak

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial…

Optimization and Control · Mathematics 2022-03-09 F. Nasresfahani , M. R. Eslahchi

The problem of indoor navigation of mobile objects, using a map and measurements of distances to the walls is considered. A nonlinear filtering problem aimed at calculating the optimal, in the root-mean-square sense, of the sought…

Robotics · Computer Science 2019-08-21 Mostafa Mansour , Oleg Stepanov

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

Numerical Analysis · Mathematics 2017-03-08 Jun Kitagawa , Quentin Mérigot , Boris Thibert

In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients.…

Numerical Analysis · Mathematics 2016-09-27 Xiaogang Zhu , Yufeng Nie

This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…

Computer Vision and Pattern Recognition · Computer Science 2015-03-17 Julien Rabin , Nicolas Papadakis

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

Optimization and Control · Mathematics 2020-10-23 Luca De Gennaro Aquino , Stephan Eckstein

We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…

Probability · Mathematics 2023-07-20 Michael Goldman , Dario Trevisan

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…

Optimization and Control · Mathematics 2023-03-03 Clara Leparoux , Riccardo Bonalli , Bruno Hérissé , Frédéric Jean

Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…

Computer Vision and Pattern Recognition · Computer Science 2020-03-17 Guansong Lu , Zhiming Zhou , Jian Shen , Cheng Chen , Weinan Zhang , Yong Yu

A variational method is presented for directly finding the bifurcation point of nonlinear equations as the saddle-node point of the extended nonlinear Rayleigh quotient. The method is applied for solving an open problem on the existence of…

Analysis of PDEs · Mathematics 2023-03-21 Yavdat Il'yasov

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…

Physics and Society · Physics 2024-10-10 Abdullahi Adinoyi Ibrahim , Michael Muehlebach , Caterina De Bacco

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…

Machine Learning · Computer Science 2023-06-06 Brandon Amos , Samuel Cohen , Giulia Luise , Ievgen Redko

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…

Optimization and Control · Mathematics 2012-11-29 Jonathan Korman , Robert J. McCann

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…

Numerical Analysis · Mathematics 2017-06-19 Jean Feydy , Benjamin Charlier , François-Xavier Vialard , Gabriel Peyré

Sensor network localization problem is to determine the position of the sensor nodes in a network given pairwise distance measurements. Such problem can be formulated as a polynomial minimization via the least squares method. This paper…

Computational Complexity · Computer Science 2013-11-22 Ning Ruan , David Y Gao

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod…

Probability · Mathematics 2016-08-04 Gaoyue Guo , Xiaolu Tan , Nizar Touzi