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In this paper we introduce new nonlinear scalarization methods to characterize minimal elements of set-valued problems equipped with variable domination structures. For certain set relations with respect to variable domination structures we give a characterization of these relations using corresponding nonlinear scalarizing functionals and the properties of these functionals. We describe different kinds of minimal elements to a family of sets with respect to variable domination structures. Furthermore we investigate a descent method to find approximations of minimal solutions of set-valued problems with respect to variable domination structures using nonlinear scalarization methods. Finally we apply the results to a set-valued problem in Medical Image Registration. |
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