A property ofbicriteria 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 co...
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Trường Đại học Đà Lạt
2012
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oai:scholar.dlu.edu.vn:DLU123456789-310682023-10-27T14:41:42Z A property ofbicriteria affine vector variational inequalities Nguyễn, Thị Thu Hương Trần, Ninh Hoà Tạ, Duy Phượng Nguyễn, Đông Yên Bicriteria affine vector variational inequality Acalarlaation Solution set Connectedness 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 2in [17] about finding an upperboundfor the numbers ofconnected components of the solution sets under investigation. Mathematics Subject Classification. 49J40, 49J53, 90C29. 2012-06-18T06:59:57Z 2012-06-18T06:59:57Z 2012 Article https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/31068 en Tạp chí Khoa học Đại học Đà Lạt, số 3a;tr. 57-62 application/pdf Trường Đại học Đà Lạt |
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Thư viện Trường Đại học Đà Lạt |
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English |
| topic |
Bicriteria affine vector variational inequality Acalarlaation Solution set Connectedness |
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Bicriteria affine vector variational inequality Acalarlaation Solution set Connectedness Nguyễn, Thị Thu Hương Trần, Ninh Hoà Tạ, Duy Phượng Nguyễn, Đông Yên A property ofbicriteria affine vector variational inequalities |
| 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
2in [17] about finding an upperboundfor the numbers ofconnected components
of the solution sets under investigation.
Mathematics Subject Classification. 49J40, 49J53, 90C29. |
| format |
Article |
| author |
Nguyễn, Thị Thu Hương Trần, Ninh Hoà Tạ, Duy Phượng Nguyễn, Đông Yên |
| author_facet |
Nguyễn, Thị Thu Hương Trần, Ninh Hoà Tạ, Duy Phượng Nguyễn, Đông Yên |
| author_sort |
Nguyễn, Thị Thu Hương |
| title |
A property ofbicriteria affine vector variational inequalities |
| title_short |
A property ofbicriteria affine vector variational inequalities |
| title_full |
A property ofbicriteria affine vector variational inequalities |
| title_fullStr |
A property ofbicriteria affine vector variational inequalities |
| title_full_unstemmed |
A property ofbicriteria affine vector variational inequalities |
| title_sort |
property ofbicriteria affine vector variational inequalities |
| publisher |
Trường Đại học Đà Lạt |
| publishDate |
2012 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/31068 |
| _version_ |
1819847433077653504 |