On G-invexity-type nonlinear programming problems
In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable op...
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| Format: | Article |
| Language: | English |
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Balikesir University
2015-01-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://ijocta.balikesir.edu.tr/index.php/files/article/view/202/112 |
| _version_ | 1828026723479846912 |
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| author | Tadeusz Antczak Manuel Arana Jiménez |
| author_facet | Tadeusz Antczak Manuel Arana Jiménez |
| author_sort | Tadeusz Antczak |
| collection | DOAJ |
| description | In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established. |
| first_indexed | 2024-04-10T13:23:37Z |
| format | Article |
| id | doaj.art-90c1199db81c4909b6953f114e45e322 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T13:23:37Z |
| publishDate | 2015-01-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-90c1199db81c4909b6953f114e45e3222023-02-15T16:11:55ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032015-01-0151132010.11121/ijocta.01.2015.00202On G-invexity-type nonlinear programming problemsTadeusz AntczakManuel Arana JiménezIn this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.http://ijocta.balikesir.edu.tr/index.php/files/article/view/202/112mathematical programmingKT-G-invexityWD-G-invexityG-Karush-Kuhn-Tucker pointG-Wolfe dual problem |
| spellingShingle | Tadeusz Antczak Manuel Arana Jiménez On G-invexity-type nonlinear programming problems An International Journal of Optimization and Control: Theories & Applications mathematical programming KT-G-invexity WD-G-invexity G-Karush-Kuhn-Tucker point G-Wolfe dual problem |
| title | On G-invexity-type nonlinear programming problems |
| title_full | On G-invexity-type nonlinear programming problems |
| title_fullStr | On G-invexity-type nonlinear programming problems |
| title_full_unstemmed | On G-invexity-type nonlinear programming problems |
| title_short | On G-invexity-type nonlinear programming problems |
| title_sort | on g invexity type nonlinear programming problems |
| topic | mathematical programming KT-G-invexity WD-G-invexity G-Karush-Kuhn-Tucker point G-Wolfe dual problem |
| url | http://ijocta.balikesir.edu.tr/index.php/files/article/view/202/112 |
| work_keys_str_mv | AT tadeuszantczak onginvexitytypenonlinearprogrammingproblems AT manuelaranajimenez onginvexitytypenonlinearprogrammingproblems |