Abstract:

The nonlinear scalarization function of sets is defined in a topological vector space with a partial order structure. Some properties of the nonlinear scalarizaiton function are proved. By means of  the nonlinear scalarization function, the authors have deduced a generalized Ekeland’s variational principle for setvalued map, which is a generalization of the vectorial form of Ekelandtype variational principle.

Key words: topological vector space； setvalued mapping； Ekeland’s principle； nonlinear scalarization function