Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/36081
Title: First- and second-order necessary conditions via exact penalty functions
Authors: Meng, KW
Yang, XQ 
Keywords: Nonlinear programming problem
KKT condition
Second-order necessary condition
Subderivative
Regular subdifferential
Issue Date: 2015
Publisher: Springer
Source: Journal of optimization theory and applications, 2015, v. 165, no. 3, p. 720-752 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: In this paper, we study first- and second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subderivative of the penalty term, we also present sufficient conditions for a penalty term to be of KKT-type. We then derive a second-order necessary condition by assuming a second-order constraint qualification, which requires that the second-order linearized tangent set is included in the closed convex hull of the kernel of the parabolic subderivative of the penalty term. In particular, for a penalty term with order , by assuming the nonpositiveness of a sum of a second-order derivative and a third-order derivative of the original data and applying a third-order Taylor expansion, we obtain the second-order necessary condition.
URI: http://hdl.handle.net/10397/36081
ISSN: 0022-3239 (print)
1573-2878 (online)
DOI: 10.1007/s10957-014-0664-x
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