Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency
In this paper, we consider, a new nonlinear scalarization function in vector spaces which is a generalization of the oriented distance function. Using the algebraic type of closure, which is called vector closure, we introduce the algebraic boundary of a set, without assuming any topology, in our co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2022-02-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/1995 |
| _version_ | 1818251986511855616 |
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| author | E. Kiyani S. M. Vaezpour J. Tavakoli |
| author_facet | E. Kiyani S. M. Vaezpour J. Tavakoli |
| author_sort | E. Kiyani |
| collection | DOAJ |
| description | In this paper, we consider, a new nonlinear scalarization function in vector spaces which is a generalization of the oriented distance function. Using the algebraic type of closure, which is called vector closure, we introduce the algebraic boundary of a set, without assuming any topology, in our context. Furthermore, some properties of this algebraic boundary set are given and present the concept of the oriented distance function via this set in the concept of vector optimization. We further investigate Q-proper efficiency in a real vector space, where Q is some nonempty (not necessarily convex) set. The necessary and sufficient conditions for Q-proper efficient solutions of nonconvex optimization problems are obtained via the scalarization technique. The scalarization technique relies on the use of two different scalarization functions, the oriented distance function and nonconvex separation function, which allow us to characterize the Q-proper efficiency in vector optimization with and without constraints. |
| first_indexed | 2024-12-12T16:17:00Z |
| format | Article |
| id | doaj.art-232b90f7e6564fb58ff4bc82bd2aa4c9 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-12T16:17:00Z |
| publishDate | 2022-02-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-232b90f7e6564fb58ff4bc82bd2aa4c92022-12-22T00:19:03ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392022-02-0120111110.28924/2291-8639-20-2022-111490Nonconvex Vector Optimization and Optimality Conditions for Proper EfficiencyE. KiyaniS. M. VaezpourJ. TavakoliIn this paper, we consider, a new nonlinear scalarization function in vector spaces which is a generalization of the oriented distance function. Using the algebraic type of closure, which is called vector closure, we introduce the algebraic boundary of a set, without assuming any topology, in our context. Furthermore, some properties of this algebraic boundary set are given and present the concept of the oriented distance function via this set in the concept of vector optimization. We further investigate Q-proper efficiency in a real vector space, where Q is some nonempty (not necessarily convex) set. The necessary and sufficient conditions for Q-proper efficient solutions of nonconvex optimization problems are obtained via the scalarization technique. The scalarization technique relies on the use of two different scalarization functions, the oriented distance function and nonconvex separation function, which allow us to characterize the Q-proper efficiency in vector optimization with and without constraints.http://etamaths.com/index.php/ijaa/article/view/1995 |
| spellingShingle | E. Kiyani S. M. Vaezpour J. Tavakoli Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency International Journal of Analysis and Applications |
| title | Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency |
| title_full | Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency |
| title_fullStr | Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency |
| title_full_unstemmed | Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency |
| title_short | Nonconvex Vector Optimization and Optimality Conditions for Proper Efficiency |
| title_sort | nonconvex vector optimization and optimality conditions for proper efficiency |
| url | http://etamaths.com/index.php/ijaa/article/view/1995 |
| work_keys_str_mv | AT ekiyani nonconvexvectoroptimizationandoptimalityconditionsforproperefficiency AT smvaezpour nonconvexvectoroptimizationandoptimalityconditionsforproperefficiency AT jtavakoli nonconvexvectoroptimizationandoptimalityconditionsforproperefficiency |