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A note on scalar-valued gap functions for generalized vector variational inequalities. (English) Zbl 1292.49013

Summary: This paper is concerned with gap functions of Generalized Vector Variational Inequalities (GVVIs). By using a scalarization approach, scalar-valued variational inequalities of GVVIs are introduced. Some relationships between the solutions of GVVIs and their scalarized versions are established. Then, by using these relationships and some mild conditions, scalar-valued gap functions for GVVIs are established.

MSC:

49J40 Variational inequalities
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