Higher-order Karush–Kuhn–Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming

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.

Keywords:

• Higher-order Karush–Kuhn–Tucker optimality conditions
• multiobjective semi-infinite programming problem
• Borwein properly efficient solutions
• higher-order Studniarski derivatives
• m-stable functions

AMS CLASSIFICATIONS:

• 90C46
• 90C29
• 49J52
• 90C34

Acknowledgments

The authors are grateful to the two anonymous referees and the associate editor for their valuable comments and suggestions, which helped to improve the quality of the paper in its present form.

Disclosure statement

No potential conflict of interest was reported by the author(s).