ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS
Multilevel optimization problems often arise in various applications (in economics, ecology, power engineering and other areas) when modeling complex systems with a hierarchical structure associated with independent actions of subsystems. The difficulty of analyzing such complex systems requires fir...
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| Format: | Article |
| Language: | Russian |
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Educational institution «Belarusian State University of Informatics and Radioelectronics»
2019-12-01
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| Series: | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
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| Online Access: | https://doklady.bsuir.by/jour/article/view/2451 |
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| _version_ | 1839567768229249024 |
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| author | L. I. Minchenko S. I. Sirotko |
| author_facet | L. I. Minchenko S. I. Sirotko |
| author_sort | L. I. Minchenko |
| collection | DOAJ |
| description | Multilevel optimization problems often arise in various applications (in economics, ecology, power engineering and other areas) when modeling complex systems with a hierarchical structure associated with independent actions of subsystems. The difficulty of analyzing such complex systems requires first of all the study of bilevel models, the management of which would be an integral part of the analysis of more complex systems. In solving bilevel programming problems, an important role is played by the property of partial calmness, the presence of which allows us to reduce the bilevel problem to the classical nonlinear programming problem with a nonsmooth objective function. It is known that linear bilevel programming problems are partially stable. The proof of this property for more complex problems meets difficulties. In particular, our article shows the inaccuracy of some results in this area. The goal of the paper is to obtain some new results in the partial calmness of bilevel programming. In particular, new sufficient conditions for bilevel problems are proved. The results are obtained on the base of Lipschitz-like properties for multivalued mappings. In the paper we propose new sufficient conditions for partial calmness which are based on some modification of the known constraint qualification RCPLD which have been proposed by the researches Andreani, Haeser, Schuverdt and Silva. |
| format | Article |
| id | doaj-art-a4fe1696e9d74b2eba79940b1bb643e9 |
| institution | Matheson Library |
| issn | 1729-7648 |
| language | Russian |
| publishDate | 2019-12-01 |
| publisher | Educational institution «Belarusian State University of Informatics and Radioelectronics» |
| record_format | Article |
| series | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| spelling | doaj-art-a4fe1696e9d74b2eba79940b1bb643e92025-08-04T17:38:20ZrusEducational institution «Belarusian State University of Informatics and Radioelectronics»Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki1729-76482019-12-0107-8869210.35596/1729-7648-2019-126-8-86-921501ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONSL. I. Minchenko0S. I. Sirotko1Belarusian State University of Informatics and RadioelectronicsBelarusian State University of Informatics and RadioelectronicsMultilevel optimization problems often arise in various applications (in economics, ecology, power engineering and other areas) when modeling complex systems with a hierarchical structure associated with independent actions of subsystems. The difficulty of analyzing such complex systems requires first of all the study of bilevel models, the management of which would be an integral part of the analysis of more complex systems. In solving bilevel programming problems, an important role is played by the property of partial calmness, the presence of which allows us to reduce the bilevel problem to the classical nonlinear programming problem with a nonsmooth objective function. It is known that linear bilevel programming problems are partially stable. The proof of this property for more complex problems meets difficulties. In particular, our article shows the inaccuracy of some results in this area. The goal of the paper is to obtain some new results in the partial calmness of bilevel programming. In particular, new sufficient conditions for bilevel problems are proved. The results are obtained on the base of Lipschitz-like properties for multivalued mappings. In the paper we propose new sufficient conditions for partial calmness which are based on some modification of the known constraint qualification RCPLD which have been proposed by the researches Andreani, Haeser, Schuverdt and Silva.https://doklady.bsuir.by/jour/article/view/2451bilevel programmingpartial calmnessregularity conditions |
| spellingShingle | L. I. Minchenko S. I. Sirotko ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki bilevel programming partial calmness regularity conditions |
| title | ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS |
| title_full | ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS |
| title_fullStr | ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS |
| title_full_unstemmed | ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS |
| title_short | ON THE PROBLEMS OF BILEVEL OPTIMIZATION UNDER RCPLD CONSTRAINT QUALIFICATIONS |
| title_sort | on the problems of bilevel optimization under rcpld constraint qualifications |
| topic | bilevel programming partial calmness regularity conditions |
| url | https://doklady.bsuir.by/jour/article/view/2451 |
| work_keys_str_mv | AT liminchenko ontheproblemsofbileveloptimizationunderrcpldconstraintqualifications AT sisirotko ontheproblemsofbileveloptimizationunderrcpldconstraintqualifications |