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A Comparison of Two Dual Methods for Discrete Optimal Transport

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8085))

Abstract

The goal of this expository article is to present and compare two dual methods that have been proposed independently for computing solutions of the discrete or semi-discrete instances of optimal transport.

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References

  1. Aurenhammer, F., Hoffmann, F., Aronov, B.: Minkowski-type theorems and least-squares clustering. Algorithmica 20(1), 61–76 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benamou, J.D., Brenier, Y.: A computational fluid mechanics solution to the monge-kantorovich mass transfer problem. Numerische Mathematik 84(3), 375–393 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benamou, J.-D., Froese, B., Oberman, A.: Numerical solution of the second boundary value problem for the Elliptic Monge-Ampère equation, Rapport de recherche (2012)

    Google Scholar 

  4. Bertsekas, D.P.: A new algorithm for the assignment problem. Mathematical Programming 21(1), 152–171 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bertsekas, D.P., Eckstein, J.: Dual coordinate step methods for linear network flow problems. Mathematical Programming 42(1), 203–243 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Burkard, R.E., Dell’Amico, M., Martello, S.: Assignment problems. Society for Industrial Mathematics (2009)

    Google Scholar 

  7. Caffarelli, L., Kochengin, S., Oliker, V.I.: On the numerical solution of the problem of reflector design with given far-field scattering data. Contemporary Mathematics 226, 13–32 (1999)

    Article  MathSciNet  Google Scholar 

  8. Cullen, M.J.P., Purser, R.J.: An extended lagrangian theory of semi-geostrophic frontogenesis. Journal of Atmospheric Sciences 41, 1477–1497 (1984)

    Article  MathSciNet  Google Scholar 

  9. Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM (JACM) 19(2), 248–264 (1972)

    Article  MATH  Google Scholar 

  10. Kitagawa, J.: An iterative scheme for solving the optimal transportation problem, arXiv preprint arXiv:1208.5172 (2012)

    Google Scholar 

  11. Loeper, G., Rapetti, F.: Numerical solution of the monge–ampère equation by a newton’s algorithm. Comptes Rendus Mathematique 340(4), 319–324 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mérigot, Q.: A multiscale approach to optimal transport. In: Computer Graphics Forum, vol. 30, pp. 1583–1592. Wiley Online Library (2011)

    Google Scholar 

  13. Oliker, V.I., Prussner, L.D.: On the numerical solution of the equation \(\frac{\partial^2 z}{\partial x} \frac{\partial^2 z}{\partial y^2} - \left(\frac{\partial^2 z}{\partial x\partial y}\right)^2=f\). Numerische Mathematik 54(3), 271–293 (1988)

    Article  MathSciNet  MATH  Google Scholar 

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Mérigot, Q. (2013). A Comparison of Two Dual Methods for Discrete Optimal Transport. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_42

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  • DOI: https://doi.org/10.1007/978-3-642-40020-9_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40019-3

  • Online ISBN: 978-3-642-40020-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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