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Existence and duality of implicit vector variational problems. (English) Zbl 1039.49003

Summary: We consider implicit vector variational problems which contain vector equilibrium problems and vector variational inequalities as special cases. The existence of solutions of implicit vector variational problems and vector equilibrium problems have been established. As a special case, we derive some existence results for a solution of vector variational inequalities. We also study the duality of implicit vector variational problems and discuss the relationship between solutions of dual and primal problems. Our results on duality contains known results in the literature as special cases.

MSC:

49J40 Variational inequalities
49N15 Duality theory (optimization)
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