Geodesic
On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 191-200

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New results are presented on the construction of exterior penalty functions of increased smoothness in linear programming and on the construction of iterative methods on their basis with automatic matching of their parameters. New constructions, similarly to interior penalty functions, make it possible to use second-order optimization methods and at the same time do not require knowledge of at least one interior admissible point of the original problem for the start of the operation. Moreover, the new penalty functions can also be applied to improper linear programming problems (problems with inconsistent constraint systems), for which they can produce generalized (compromise) solutions. Convergence theorems are proved and data of numerical experiments are presented.
Keywords: linear programming, improper (ill-posed) problems, generalized solutions, penalty functions method, Newton method. 
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     author = {L. D. Popov},
     title = {On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions},
     journal = {Trudy Instituta matematiki i mehaniki},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/}
}
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L. D. Popov. On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 191-200. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a17/