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Scalarization and optimality conditions for vector equilibrium problems. (English) Zbl 1197.49011
Summary: We investigate vector equilibrium problems and give scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provide necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we give sufficient conditions for those solutions. As applications, necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems are provided.

MSC:
49J52 Nonsmooth analysis
49J50 Fréchet and Gateaux differentiability in optimization
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
49K27 Optimality conditions for problems in abstract spaces
49N15 Duality theory (optimization)
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