Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65424
Title: Variational analysis on local sharp minima via exact penalization
Authors: Meng, K
Yang, X 
Keywords: Exact penalization
Local sharp minimum
Regular subdifferential
Smallest penalty parameter
Subderivative
Issue Date: 2016
Publisher: Springer
Source: Set-valued and variational analysis, 2016, v. 24, no. 4, p. 619-635 How to cite?
Journal: Set-valued and variational analysis 
Abstract: In this paper we study local sharp minima of the nonlinear programming problem via exact penalization. Utilizing generalized differentiation tools in variational analysis such as subderivatives and regular subdifferentials, we obtain some primal and dual characterizations for a penalty function associated with the nonlinear programming problem to have a local sharp minimum. These general results are then applied to the ?p penalty function with 0 ? p ? 1. In particular, we present primal and dual equivalent conditions in terms of the original data of the nonlinear programming problem, which guarantee that the ?p penalty function has a local sharp minimum with a finite penalty parameter in the case of p?(12,1] and p=12 respectively. By assuming the Guignard constraint qualification (resp. the generalized Guignard constraint qualification), we also show that a local sharp minimum of the nonlinear programming problem can be an exact local sharp minimum of the ?p penalty function with p ? [0, 1] (resp. p?[0,12]). Finally, we give some formulas for calculating the smallest penalty parameter for a penalty function to have a local sharp minimum.
URI: http://hdl.handle.net/10397/65424
ISSN: 1877-0533
EISSN: 1877-0541
DOI: 10.1007/s11228-016-0360-0
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

18
Last Week
3
Last month
Checked on Oct 16, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.