Journal of Convex Analysis 22 (2015), No. 3, 797--808
Copyright Heldermann Verlag 2015
An Elementary Approach to Linear Programming Duality with Application to Capacity Constrained Transport
Jonathan Korman
Dept. of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
jkorman@math.toronto.edu
Robert J. McCann
Dept. of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
mccann@math.toronto.edu
Christian Seis
Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
cseis@math.toronto.edu
An 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.
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