Geodesic
On one method of increasing the smoothness of external penalty functions in linear and convex programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 88-101

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We propose original constructions of external penalty functions in linear and convex programming, which asymptotically reduce constrained optimization problems to unconstrained ones with increased smoothness. The latter admit an effective solution by second-order methods and, at the same time, do not require the knowledge of an interior feasible point of the original problem to start the process. Moreover, the proposed approach is applicable to improper linear and convex programs (problems with contradictory constraint systems), for which they can generate some generalized (compromise) solutions. Convergence theorems and the data of numerical experiments are presented.
Keywords: linear programming, improper (ill-posed) problems, generalized solutions, penalty functions, Newton method. 
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     author = {L. D. Popov},
     title = {On one method of increasing the smoothness of external penalty functions in linear and convex programming},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {88--101},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a6/}
}
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L. D. Popov. On one method of increasing the smoothness of external penalty functions in linear and convex programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 4, pp. 88-101. http://geodesic.mathdoc.fr/item/TIMM_2021_27_4_a6/