publication . Preprint . 2013

A penalization approach to linear programming duality with application to capacity constrained transport

Korman, Jonathan; McCann, Robert J.; Seis, Christian;
Open Access English
  • Published: 11 Sep 2013
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.
free text keywords: Mathematics - Optimization and Control, Mathematics - Analysis of PDEs
Funded by
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
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[1] Bethuel, F., Brezis, H., and H´elein, F. Ginzburg-Landau vortices. Progress in Nonlinear Differential Equations and their Applications, 13. Birkh¨auser Boston Inc., Boston, MA, 1994. [OpenAIRE]

[2] Kantorovich, L. On the translocation of masses. C.R. (Doklady) Acad. Sci. URSS (N.S.) 37 (1942), 199-201.

[3] Kellerer, H. G. Marginalprobleme fu¨r Funktionen. Math. Ann. 154 (1964), 147-156.

[4] Kellerer, H. G. Maßtheoretische Marginalprobleme. Math. Ann. 153 (1964), 168-198.

[5] Korman, J., and McCann, R. J. Optimal transport with capacity constraints. Preprint arXiv:1201.6404, 2012.

[6] Korman, J., and McCann, R. J. Insights into capacity constrained optimal transport. Proc. Natl. Acad. Sci. USA 110 (2013), 10064-10067. [OpenAIRE]

[7] Korman, J., McCann, R. J., and Seis, C. Dual measures for capacity constrained optimal transport. Preprint arXiv:1307.7774, 2013.

[8] Levin, V. L. The problem of mass transfer in a topological space and probability measures with given marginal measures on the product of two spaces. Dokl. Akad. Nauk SSSR 276, 5 (1984), 1059-1064.

[9] Luenberger, D. G., and Ye, Y. Linear and nonlinear programming, third ed. International Series in Operations Research & Management Science, 116. Springer, New York, 2008. [OpenAIRE]

[10] Monge, G. M´emoire sur la th´eorie de d´eblais et de remblais. Histoire de l'Acad´emie Royale des Science de Paris, avec les M´emoires de Math´ematique et de Physique pour la mˆeme ann´ee (1781), 666-704.

[11] Mugnai, L., Seis, C., and Spadaro, E. Global solutions to the volume-preserving mean-curvature flow. In preparation, 2013.

[12] Rachev, S. T., and Ru¨schendorf, L. Mass transportation problems. Vol. I. Probability and its Applications (New York). Springer-Verlag, New York, 1998. Theory.

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