Necessary optimality conditions for a bilevel multiobjective problem in terms of approximations

Abstract

In this work, we are concerned with a bilevel multiobjective optimization problem. To get the Karush–Kuhn–Tucker-type necessary optimality condition, with the help of the generalized Motzkin's Theorem, we introduced an appropriate generalized constraint qualification. Our findings are based on a mean-value theorem in terms of approximations for continuous functions. Examples that illustrate our results are also given.