A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES
By a scalarization method, it is proved that both the Pareto solution set and the weak Pareto solution set of a bicriteria affine vector variational inequality have finitely many connected. components provided that a regularity condition is satisfied. An explicit upper bound for the numbers of conne...
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| Format: | Article |
| Language: | English |
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Dalat University
2012-06-01
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| Series: | Tạp chí Khoa học Đại học Đà Lạt |
| Subjects: | |
| Online Access: | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/198 |
| _version_ | 1798028474803290112 |
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| author | Nguyễn Thị Thu Hương Trần Ninh Hoa Tạ Duy Phượng Nguyễn Đông Yên |
| author_facet | Nguyễn Thị Thu Hương Trần Ninh Hoa Tạ Duy Phượng Nguyễn Đông Yên |
| author_sort | Nguyễn Thị Thu Hương |
| collection | DOAJ |
| description | By a scalarization method, it is proved that both the Pareto solution set and the weak Pareto solution set of a bicriteria affine vector variational inequality have finitely many connected. components provided that a regularity condition is satisfied. An explicit upper bound for the numbers of connected components of the Pareto solution set and the weak. Pareto solution set is obtained. Consequences of the results for bicriteria quadratic vector optimization problems and linear fractional vector optimization problems are discussed in detail. Under an additional assumption on the data set, Theorems 3.1 and 3.2 in this paper solve in the affirmative Question 1 in [17, p. 66] and Question 9.3 in [151 for the case of bicriteria problems without requiring the monotonicity. Besides, the theorems also give a partial solution to Question 2 in [17] about finding an upperboundfor the numbers ofconnected components of the solution sets under investigation. |
| first_indexed | 2024-04-11T19:09:52Z |
| format | Article |
| id | doaj.art-77f3fd5f8ce94ef4a1d12ec9e65b0431 |
| institution | Directory Open Access Journal |
| issn | 0866-787X |
| language | English |
| last_indexed | 2024-04-11T19:09:52Z |
| publishDate | 2012-06-01 |
| publisher | Dalat University |
| record_format | Article |
| series | Tạp chí Khoa học Đại học Đà Lạt |
| spelling | doaj.art-77f3fd5f8ce94ef4a1d12ec9e65b04312022-12-22T04:07:40ZengDalat UniversityTạp chí Khoa học Đại học Đà Lạt0866-787X2012-06-012210.37569/DalatUniversity.2.2.198(2012)A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIESNguyễn Thị Thu Hương0Trần Ninh Hoa1Tạ Duy Phượng2Nguyễn Đông Yên3Department of Information Technology, Le Quy Don UniversityHanoi-Amsterdam High SchoolInstitute of Mathematics, Vietnamese Academy of Science and TechnologyInstitute of Mathematics, Vietnamese Academy of Science and TechnologyBy a scalarization method, it is proved that both the Pareto solution set and the weak Pareto solution set of a bicriteria affine vector variational inequality have finitely many connected. components provided that a regularity condition is satisfied. An explicit upper bound for the numbers of connected components of the Pareto solution set and the weak. Pareto solution set is obtained. Consequences of the results for bicriteria quadratic vector optimization problems and linear fractional vector optimization problems are discussed in detail. Under an additional assumption on the data set, Theorems 3.1 and 3.2 in this paper solve in the affirmative Question 1 in [17, p. 66] and Question 9.3 in [151 for the case of bicriteria problems without requiring the monotonicity. Besides, the theorems also give a partial solution to Question 2 in [17] about finding an upperboundfor the numbers ofconnected components of the solution sets under investigation.https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/198Bicriteria affine vector variational inequalityAcalarlaationSolution setConnectednessNumber of connected components |
| spellingShingle | Nguyễn Thị Thu Hương Trần Ninh Hoa Tạ Duy Phượng Nguyễn Đông Yên A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES Tạp chí Khoa học Đại học Đà Lạt Bicriteria affine vector variational inequality Acalarlaation Solution set Connectedness Number of connected components |
| title | A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES |
| title_full | A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES |
| title_fullStr | A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES |
| title_full_unstemmed | A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES |
| title_short | A PROPERTY OF BICRITERIA AFFINE VECTOR VARIATIONAL INEQUALITIES |
| title_sort | property of bicriteria affine vector variational inequalities |
| topic | Bicriteria affine vector variational inequality Acalarlaation Solution set Connectedness Number of connected components |
| url | https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/198 |
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