An Elementary Approach to Linear Programming Duality with Application to Capacity Constrained Transport
Jonathan Korman, Robert J. McCann, Christian Seis · Journal of convex analysis · 2015
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