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Disconnectedness and unboundedness of the solution sets of monotone vector variational inequalities. (English) Zbl 1456.49011

Summary: In this paper, we investigate the topological structure of solution sets of monotone vector variational inequalities (VVIs). We show that if the weak Pareto solution set of a monotone VVI is disconnected, then each connected component of the set is unbounded. Similarly, this property holds for the proper Pareto solution set. Two open questions on the topological structure of the solution sets of (symmetric) monotone VVIs are raised at the end of the paper.

MSC:

49J40 Variational inequalities
47H05 Monotone operators and generalizations
90C29 Multi-objective and goal programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
54D05 Connected and locally connected spaces (general aspects)
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