Numerical enclosures of the optimal cost of the Kantorovitch’s mass transportation problem

Nicolas Delanoue (), Mehdi Lhommeau () and Philippe Lucidarme ()

Computational Optimization and Applications, 2016, vol. 63, issue 3, 855-873

Abstract: The problem of optimal transportation was formalized by the French mathematician Gaspard Monge in 1781. Since Kantorovitch, this (generalized) problem is formulated with measure theory. Based on Interval Arithmetic, we propose a guaranteed discretization of the Kantorovitch’s mass transportation problem. Our discretization is spatial: supports of the two mass densities are partitioned into finite families. The problem is relaxed to a finite dimensional linear programming problem whose optimum is a lower bound to the optimum of the initial one. Based on Kantorovitch duality and Interval Arithmetic, a method to obtain an upper bound to the optimum is also provided. Preliminary results show that good approximations are obtained. Copyright Springer Science+Business Media New York 2016

Keywords: Optimal transportation; Interval arithmetic; Continuous programming; Optimization (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-015-9794-9 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:63:y:2016:i:3:p:855-873

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9794-9

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().