Approximations of objective function and constraints in bi-criteria optimization problems
In this paper we study approximation methods for solving bi-criteria optimization problems. Initial problem is approximated by a new one which has the components of the objective and the constraints are replaced by their approximation functions. Components of the objective function are first and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2018-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/1153 |
| _version_ | 1818520861865410560 |
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| author | Traian Ionut Luca Dorel I. Duca |
| author_facet | Traian Ionut Luca Dorel I. Duca |
| author_sort | Traian Ionut Luca |
| collection | DOAJ |
| description |
In this paper we study approximation methods for solving bi-criteria optimization problems.
Initial problem is approximated by a new one which has the components of the objective and the constraints are replaced by their approximation functions. Components of the objective function are first and second order approximated and constraints are first order approximated. Conditions such that efficient solution of the approximate problem will remain efficient for initial problem and reciprocally are studied.
Numerical examples are developed to emphasize the importance of these conditions.
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| first_indexed | 2024-12-11T01:43:18Z |
| format | Article |
| id | doaj.art-5d403f74e41d4fa181c839bca821db6a |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T01:43:18Z |
| publishDate | 2018-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-5d403f74e41d4fa181c839bca821db6a2022-12-22T01:24:59ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2018-12-01472Approximations of objective function and constraints in bi-criteria optimization problemsTraian Ionut Luca0Dorel I. Duca1Babes-Bolyai UniversityBabes-Bolyai University In this paper we study approximation methods for solving bi-criteria optimization problems. Initial problem is approximated by a new one which has the components of the objective and the constraints are replaced by their approximation functions. Components of the objective function are first and second order approximated and constraints are first order approximated. Conditions such that efficient solution of the approximate problem will remain efficient for initial problem and reciprocally are studied. Numerical examples are developed to emphasize the importance of these conditions. https://www.ictp.acad.ro/jnaat/journal/article/view/1153efficient solutionbi-criteria optimizationeta-approximationinvex functionincave functionoptimization |
| spellingShingle | Traian Ionut Luca Dorel I. Duca Approximations of objective function and constraints in bi-criteria optimization problems Journal of Numerical Analysis and Approximation Theory efficient solution bi-criteria optimization eta-approximation invex function incave function optimization |
| title | Approximations of objective function and constraints in bi-criteria optimization problems |
| title_full | Approximations of objective function and constraints in bi-criteria optimization problems |
| title_fullStr | Approximations of objective function and constraints in bi-criteria optimization problems |
| title_full_unstemmed | Approximations of objective function and constraints in bi-criteria optimization problems |
| title_short | Approximations of objective function and constraints in bi-criteria optimization problems |
| title_sort | approximations of objective function and constraints in bi criteria optimization problems |
| topic | efficient solution bi-criteria optimization eta-approximation invex function incave function optimization |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/1153 |
| work_keys_str_mv | AT traianionutluca approximationsofobjectivefunctionandconstraintsinbicriteriaoptimizationproblems AT doreliduca approximationsofobjectivefunctionandconstraintsinbicriteriaoptimizationproblems |