Abstract
In this paper, vector complementarity problems are introduced as weak versions of vector variational inequalities in ordered Banach spaces. New dual cones are introduced and proved to be closed. In the sense of efficient point, we prove that the minimal element problem is solvable if a vector variational inequality is solvable; we also prove that any solution of a strong vector variational inequality or positive vector complementarity problem is a solution of the minimal element problem.
Original language | English |
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Pages (from-to) | 483-495 |
Number of pages | 13 |
Journal | Journal of Optimization Theory and Applications |
Volume | 77 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jun 1993 |
Externally published | Yes |
Keywords
- dual cones
- minimal element problems
- Vector complementarity problems
- vector variational inequalities
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics