L.D. Popov. On parameter control in iterative linear programming methods based on a new class of smooth exterior penalty functions ... P. 191-200

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

Received July 19, 2022

Revised September 21, 2022

Accepted September 26, 2022

Funding Agency: The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2022-874).

Leonid Denisovich Popov, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620000 Russia, e-mail: popld@imm.uran.ru

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Cite this article as: 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 Mekhaniki UrO RAN, 2022, vol. 28, no. 4, pp. 191–200