New Higher-Order Strong Karush-Kuhn-Tucker Conditions for Proper Solutions in Nonsmooth Optimization

摘要

This paper considers higher-order necessary conditions for Henig-proper, positively proper and Benson-proper solutions. Under suitable constraint qualifications, our conditions are of the Karush-Kuhn-Tucker rule. The conditions include higher-order complementarity slackness for both the objective and the constraining maps. They are in a nonclassical form with a supremum expression on the right-hand side (instead of zero). Our results are new and improve the existing ones in the literature, even when applied to special cases of multiobjective single-valued optimization problems.