A new minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem

Abstract In this paper, we first introduce some types of set relations on the power set of n-dimensional Euclidean spaces which are proposed by Kuroiwa-Tanaka-Ha and Jahn-Ha. We also mension new types of cancellation laws of set relations. Second, we introduce a complete lattice-valued problem on the power set of n-dimensional Euclidean spaces proposed by Hamel et al. Applying nonlinear scalrizing technique in complete lattice, we present a new type of minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem. AMS Subject Classification: 06B23, 06F30, 49J53, 58E17.