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Related papers: A Homotopy Algorithm for Optimal Transport

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This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…

Systems and Control · Computer Science 2016-03-10 Jung-Su Ha , Han-Lim Choi

Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…

Optimization and Control · Mathematics 2024-03-11 Xun Tang , Holakou Rahmanian , Michael Shavlovsky , Kiran Koshy Thekumparampil , Tesi Xiao , Lexing Ying

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on…

Physics and Society · Physics 2009-11-13 Yong Yu , Bogdan Danila , John A. Marsh , Kevin E. Bassler

In this paper we present a method for automatically planning optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition system. The…

Robotics · Computer Science 2015-03-13 Alphan Ulusoy , Stephen L. Smith , Xu Chu Ding , Calin Belta , Daniela Rus

The main contribution of this paper is the proof of the convexity of the omni-directional tethered robot workspace (namely, the set of all tether-length-admissible robot configurations), as well as a set of distance-optimal tethered path…

Robotics · Computer Science 2022-08-09 Tong Yang , Rong Xiong , Yue Wang

We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…

Algebraic Geometry · Mathematics 2025-09-11 Paul Breiding , Taylor Brysiewicz , Hannah Friedman

We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…

Optimization and Control · Mathematics 2020-05-06 Matt Jacobs , Flavien Léger

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…

Data Structures and Algorithms · Computer Science 2020-07-07 Yihe Dong , Yu Gao , Richard Peng , Ilya Razenshteyn , Saurabh Sawlani

The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…

Optimization and Control · Mathematics 2022-05-05 A. Dutta , Bharat Kumar , Deepmala , A. K. Das

This paper presents evolutionary methods for optimization in dynamic mobile robot path planning. In dynamic mobile path planning, the goal is to find an optimal feasible path from starting point to target point with various obstacles, as…

Robotics · Computer Science 2019-02-12 Masoud Fetanat , Sajjad Haghzad , Saeed Bagheri Shouraki

Discovering an optimal route to the most feasible parking lot has been a matter of concern for any driver which aggravates further during peak hours of the day and at congested places leading to considerable wastage of time and fuel. This…

Neural and Evolutionary Computing · Computer Science 2020-03-30 Romit S Beed , Sunita Sarkar , Arindam Roy

This survey article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal…

Optimization and Control · Mathematics 2017-01-24 Jiamin Zhu , Emmanuel Trélat , Max Cerf

In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…

Statistics Theory · Mathematics 2025-06-25 Sivaraman Balakrishnan , Tudor Manole , Larry Wasserman

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we…

Classical Analysis and ODEs · Mathematics 2010-09-20 Olivier Besson , Martine Picq , Jérôme Pousin

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

Machine Learning · Computer Science 2023-11-02 Nikita Gushchin , Alexander Kolesov , Alexander Korotin , Dmitry Vetrov , Evgeny Burnaev

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…

Robotics · Computer Science 2017-11-21 Shuai D Han , Nicholas M Stiffler , Athanasios Krontiris , Kostas E Bekris , Jingjin Yu

In this paper, we present a novel approach to efficiently generate collision-free optimal trajectories for multiple non-holonomic mobile robots in obstacle-rich environments. Our approach first employs a graph-based multi-agent path planner…

Robotics · Computer Science 2021-01-29 Juncheng Li , Maopeng Ran , Lihua Xie

We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…

Robotics · Computer Science 2015-12-08 Jingjin Yu

Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…

Probability · Mathematics 2023-04-26 Stephan Eckstein , Gudmund Pammer

We consider problems in which a mobile robot samples an unknown function defined over its operating space, so as to find a global optimum of this function. The path traveled by the robot matters, since it influences energy and time…

Robotics · Computer Science 2023-12-19 Tudor Santejudean , Lucian Busoniu