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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 12
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Articles

Higher order optimality conditions for inequality-constrained problems

Pages 2600-2617 | Received 03 Aug 2012, Accepted 16 Nov 2012, Published online: 06 Feb 2013
 

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 .

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Acknowledgment

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

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