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A real‐valued auction algorithm for optimal transport
Author(s) -
Walsh Joseph D.,
Dieci Luca
Publication year - 2019
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11443
Subject(s) - auction algorithm , computer science , mathematical optimization , flow network , integer (computer science) , algorithm , auction theory , mathematics , common value auction , revenue equivalence , statistics , programming language
Optimal transportation theory is an area of mathematics with real‐world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems, based on classical auction methods. Auction methods were originally developed as an alternative to the Hungarian method for the assignment problem, so the classic auction‐based algorithms solve integer‐valued optimal transport by converting such problems into assignment problems. The general transport auction method we propose works directly on real‐valued transport problems. Our results prove termination, bound the transport error, and relate our algorithm to the classic algorithms of Bertsekas and Castañón.