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An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems. (English) Zbl 1128.49008
Summary: In this paper, the notion of gap functions is extended from scalar case to vector one. Then, gap functions and generalized functions for several kinds of vector equilibrium problems are shown. As an application, the dual problem of a class of optimization problems with a system of vector equilibrium constraints (in short, OP) is established, the concavity of the dual function, the weak duality of (OP) and the saddle point sufficient condition are derived by using generalized gap functions.
MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
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