Higher order optimality conditions for inequality-constrained problems

Abstract

In this paper, we obtain higher order optimality conditions of Fritz John and Karush–Kuhn–Tucker types for the problem with inequality constraints in terms of higherorder Dini directional derivatives. In the necessary conditions, we suppose that the derivatives of order ( is a positive integer) and lower exist, and they are finite. In the sufficient ones, we assume additionally that the objective function is pseudoinvex of order with respect to some known map , and the constraints are prequasiinvex with respect to the same .

Keywords:

• nonsmooth analysis
• nonsmooth optimization
• KKT optimality conditions
• Higher order critical direction
• Higher order Mangasarian–Fromovitz constraint qualification
• higher order pseudoinvex function

AMS Subject Classifications:

• 49J52
• 90C46
• 90C30
• 26B25
• 90C26

View correction statement:

Erratum

Acknowledgment

This research is partially supported by the TU Varna Grant No. 18/2012.