Optimization Problems with Averaging over the Variables
The problems of nonlinear programming, criteria and limitations depend on the variables averaged. It is shown that if these problems have solutions, the Lagrangian reaches the maximum for the variables, which are averaged. The functions defining the problem can not be differentiable and continuous on...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2017-04-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/511 |
| _version_ | 1826559113681698816 |
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| author | Anatoly M. Tsirlin |
| author_facet | Anatoly M. Tsirlin |
| author_sort | Anatoly M. Tsirlin |
| collection | DOAJ |
| description | The problems of nonlinear programming, criteria and limitations depend on the variables averaged. It is shown that if these problems have solutions, the Lagrangian reaches the maximum for the variables, which are averaged. The functions defining the problem can not be differentiable and continuous on these variables, the set of possible values may contain isolated points. In variational problems there can be no solution in the class of piecewise continuous functions of the variables, but there can be a generalized solution in which these variables change in the sliding mode, and the optimality criterion tends to its upper edge. If in such problems the solution in the class of piecewise - continuous functions exists, the conditions of optimality of this solution are in the form of the Hamiltonian function of the maximum principle. The relationship between the average over time and across multiple variables is considered. |
| first_indexed | 2024-04-10T02:26:26Z |
| format | Article |
| id | doaj.art-c7718a0b978b482ebc33e935e862c8d8 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:55:14Z |
| publishDate | 2017-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-c7718a0b978b482ebc33e935e862c8d82025-03-02T12:46:50ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172017-04-0124222723810.18255/1818-1015-2017-2-227-238364Optimization Problems with Averaging over the VariablesAnatoly M. Tsirlin0Program Systems Institute of RASThe problems of nonlinear programming, criteria and limitations depend on the variables averaged. It is shown that if these problems have solutions, the Lagrangian reaches the maximum for the variables, which are averaged. The functions defining the problem can not be differentiable and continuous on these variables, the set of possible values may contain isolated points. In variational problems there can be no solution in the class of piecewise continuous functions of the variables, but there can be a generalized solution in which these variables change in the sliding mode, and the optimality criterion tends to its upper edge. If in such problems the solution in the class of piecewise - continuous functions exists, the conditions of optimality of this solution are in the form of the Hamiltonian function of the maximum principle. The relationship between the average over time and across multiple variables is considered.https://www.mais-journal.ru/jour/article/view/511the average optimizationexpansion of the set of admissible equivalence extensionvariation of probability measuresthe conditions in the form of the maximum principle |
| spellingShingle | Anatoly M. Tsirlin Optimization Problems with Averaging over the Variables Моделирование и анализ информационных систем the average optimization expansion of the set of admissible equivalence extension variation of probability measures the conditions in the form of the maximum principle |
| title | Optimization Problems with Averaging over the Variables |
| title_full | Optimization Problems with Averaging over the Variables |
| title_fullStr | Optimization Problems with Averaging over the Variables |
| title_full_unstemmed | Optimization Problems with Averaging over the Variables |
| title_short | Optimization Problems with Averaging over the Variables |
| title_sort | optimization problems with averaging over the variables |
| topic | the average optimization expansion of the set of admissible equivalence extension variation of probability measures the conditions in the form of the maximum principle |
| url | https://www.mais-journal.ru/jour/article/view/511 |
| work_keys_str_mv | AT anatolymtsirlin optimizationproblemswithaveragingoverthevariables |