
Journal of Convex Analysis 22 (2015), No. 3, 797808 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 capacityconstrained optimal transport as an infinitedimensional application. [ Fulltextpdf (130 KB)] for subscribers only. 