Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem
In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | International Journal for Simulation and Multidisciplinary Design Optimization |
| Subjects: | |
| Online Access: | https://www.ijsmdo.org/articles/smdo/full_html/2019/01/smdo180016/smdo180016.html |
| _version_ | 1818615776988364800 |
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| author | Hassan Mansur Baharum Adam |
| author_facet | Hassan Mansur Baharum Adam |
| author_sort | Hassan Mansur |
| collection | DOAJ |
| description | In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions. |
| first_indexed | 2024-12-16T16:39:17Z |
| format | Article |
| id | doaj.art-b52810e940cd4dd5a9baba3a410b979d |
| institution | Directory Open Access Journal |
| issn | 1779-6288 |
| language | English |
| last_indexed | 2024-12-16T16:39:17Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | International Journal for Simulation and Multidisciplinary Design Optimization |
| spelling | doaj.art-b52810e940cd4dd5a9baba3a410b979d2022-12-21T22:24:22ZengEDP SciencesInternational Journal for Simulation and Multidisciplinary Design Optimization1779-62882019-01-0110A1010.1051/smdo/2019010smdo180016Modified Courant-Beltrami penalty function and a duality gap for invex optimization problemHassan MansurBaharum AdamIn this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.https://www.ijsmdo.org/articles/smdo/full_html/2019/01/smdo180016/smdo180016.htmlCourant-Beltrami penalty functionpenalized problemLagrangian dual |
| spellingShingle | Hassan Mansur Baharum Adam Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem International Journal for Simulation and Multidisciplinary Design Optimization Courant-Beltrami penalty function penalized problem Lagrangian dual |
| title | Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem |
| title_full | Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem |
| title_fullStr | Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem |
| title_full_unstemmed | Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem |
| title_short | Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem |
| title_sort | modified courant beltrami penalty function and a duality gap for invex optimization problem |
| topic | Courant-Beltrami penalty function penalized problem Lagrangian dual |
| url | https://www.ijsmdo.org/articles/smdo/full_html/2019/01/smdo180016/smdo180016.html |
| work_keys_str_mv | AT hassanmansur modifiedcourantbeltramipenaltyfunctionandadualitygapforinvexoptimizationproblem AT baharumadam modifiedcourantbeltramipenaltyfunctionandadualitygapforinvexoptimizationproblem |