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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:
49J52Nonsmooth analysis (other weak concepts of optimality)
49J50Fréchet and Gateaux differentiability
90C29Multi-objective programming; goal programming
90C46Optimality conditions, duality
49K27Optimal control problems in abstract spaces (optimality conditions)
49N15Duality theory (optimization)