Abstract
ABSTRACT The notions of higher-order Studniarski derivative and m-stable functions (m is a positive integer) are introduced for dealing with multiobjective semi-infinite programming problem with inequality constraints. In order to obtain results on necessary optimality conditions of higher order, we study two generalized Abadie constraint qualifications for these notions together with the existence results of Studniarski derivative of higher order. An application of these constraint qualifications for the Borwein properly efficient solution on weak and strong Karush–Kuhn–Tucker necessary optimality conditions via the higher-order Studniarski derivatives with m-stable functions is presented. A higher-order sufficient optimality condition which is very close to higher-order strong Karush–Kuhn–Tucker necessary conditions to such problem is provided as well. Several examples are also constructed to illustrate the main results of the paper.
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