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A nonlinear scalarization function and generalized quasi-vector equilibrium problems. (English) Zbl 1130.90413
Summary: Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems.
MSC:
90C47Minimax problems
46N10Applications of functional analysis in optimization and programming
90C29Multi-objective programming; goal programming
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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