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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| Những tác giả chính: | , , , |
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| Định dạng: | Bài viết |
| Ngôn ngữ: | English |
| Được phát hành: |
Trường Đại học Đà Lạt
2012
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| Những chủ đề: | |
| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/31068 |
| Các nhãn: |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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| Tóm tắt: | 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. |
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