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Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces. (English) Zbl 1143.58007

Authors’ abstract: We introduce and discuss the notion of \(\varepsilon\)-solutions of vector variational inequalities. Using convex analysis and nonsmooth analysis, we provide some sufficient conditions and necessary conditions for a point to be an \(\varepsilon\)-solution of vector variational inequalities.

MSC:

58E35 Variational inequalities (global problems) in infinite-dimensional spaces
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
90C46 Optimality conditions and duality in mathematical programming
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