Geodesic
Interior penalty functions and duality in linear programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 83-89

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Logarithmic additive terms of barrier type with a penalty parameter are included into the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problem statements are formulated.
Keywords: linear programming, uality, inner penalty functions. 
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     title = {Interior penalty functions and duality in linear programming},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a9/}
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I. I. Eremin; L. D. Popov. Interior penalty functions and duality in linear programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 83-89. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a9/