A cutting-plane method with internal iteration points for the general convex programming problem
A cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-01-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/11 |
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| _version_ | 1832543051933810688 |
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| author | I. Ya. Zabotin K. E. Kazaeva O. N. Shulgina |
| author_facet | I. Ya. Zabotin K. E. Kazaeva O. N. Shulgina |
| author_sort | I. Ya. Zabotin |
| collection | DOAJ |
| description | A cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is constructed within the admissible region. At each step, it is also possible to assess how close the current value of the function is to the optimal value. The convergence of the method was proved. A few of its implementations were outlined. |
| format | Article |
| id | doaj-art-e9d561796fd04a58a60535d0880085b7 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-e9d561796fd04a58a60535d0880085b72025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-01-01165320821810.26907/2541-7746.2023.3.208-21810A cutting-plane method with internal iteration points for the general convex programming problemI. Ya. Zabotin0K. E. Kazaeva1O. N. Shulgina2Kazan Federal UniversityKazan Federal UniversityKazan Federal UniversityA cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is constructed within the admissible region. At each step, it is also possible to assess how close the current value of the function is to the optimal value. The convergence of the method was proved. A few of its implementations were outlined.https://uzakufismat.elpub.ru/jour/article/view/11convex programmingconditional minimizationoptimal valueset approximationfunction epigraphiteration pointsequence of approximationscutting hyperplaneconvergence |
| spellingShingle | I. Ya. Zabotin K. E. Kazaeva O. N. Shulgina A cutting-plane method with internal iteration points for the general convex programming problem Учёные записки Казанского университета: Серия Физико-математические науки convex programming conditional minimization optimal value set approximation function epigraph iteration point sequence of approximations cutting hyperplane convergence |
| title | A cutting-plane method with internal iteration points for the general convex programming problem |
| title_full | A cutting-plane method with internal iteration points for the general convex programming problem |
| title_fullStr | A cutting-plane method with internal iteration points for the general convex programming problem |
| title_full_unstemmed | A cutting-plane method with internal iteration points for the general convex programming problem |
| title_short | A cutting-plane method with internal iteration points for the general convex programming problem |
| title_sort | cutting plane method with internal iteration points for the general convex programming problem |
| topic | convex programming conditional minimization optimal value set approximation function epigraph iteration point sequence of approximations cutting hyperplane convergence |
| url | https://uzakufismat.elpub.ru/jour/article/view/11 |
| work_keys_str_mv | AT iyazabotin acuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem AT kekazaeva acuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem AT onshulgina acuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem AT iyazabotin cuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem AT kekazaeva cuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem AT onshulgina cuttingplanemethodwithinternaliterationpointsforthegeneralconvexprogrammingproblem |