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An Elementary Approach to Linear Programming Duality with Application to Capacity Constrained Transport
Journal of convex analysis, Tome 22 (2015) no. 3, pp. 797-808
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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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     author = {J. Korman and R. J. McCann and C. Seis},
     title = {An {Elementary} {Approach} to {Linear} {Programming} {Duality} with {Application} to {Capacity} {Constrained} {Transport}},
     journal = {Journal of convex analysis},
     pages = {797--808},
     year = {2015},
     volume = {22},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a10/}
}
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J. Korman; R. J. McCann; C. Seis. An Elementary Approach to Linear Programming Duality with Application to Capacity Constrained Transport. Journal of convex analysis, Tome 22 (2015) no. 3, pp. 797-808. http://geodesic.mathdoc.fr/item/JCA_2015_22_3_JCA_2015_22_3_a10/