Geodesic
Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 231-237

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A novel dual approach to the problem of optimal correction of first-kind improper linear programming problems with respect to their right-hand sides is proposed. It is based on the extension of the traditional Lagrangian by introducing additional regularization and barrier components. Convergence theorems are given for methods based on the augmented Lagrangian, an informal interpretation of the obtained generalized solution is suggested, and results of numerical experiments are presented.
Keywords: linear programming, improper problems, generalized solutions, barrier function method. 
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     author = {L. D. Popov},
     title = {Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a21/}
}
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L. D. Popov. Dual approach to the application of barrier functions for the optimal correction of improper linear programming problems of the first kind. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 231-237. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a21/