On the Convergence of a Smooth Penalty Algorithm without Computing Global Solutions
Joint Authors
Wang, Changyu
Liu, Bingzhuang
Zhao, Wenling
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-27
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We consider a smooth penalty algorithm to solve nonconvex optimization problem based on a family of smooth functions that approximate the usual exact penalty function.
At each iteration in the algorithm we only need to find a stationary point of the smooth penalty function, so the difficulty of computing the global solution can be avoided.
Under a generalized Mangasarian-Fromovitz constraint qualification condition (GMFCQ) that is weaker and more comprehensive than the traditional MFCQ, we prove that the sequence generated by this algorithm will enter the feasible solution set of the primal problem after finite times of iteration, and if the sequence of iteration points has an accumulation point, then it must be a Karush-Kuhn-Tucker (KKT) point.
Furthermore, we obtain better convergence for convex optimization problem.
American Psychological Association (APA)
Liu, Bingzhuang& Wang, Changyu& Zhao, Wenling. 2012. On the Convergence of a Smooth Penalty Algorithm without Computing Global Solutions. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-993425
Modern Language Association (MLA)
Liu, Bingzhuang…[et al.]. On the Convergence of a Smooth Penalty Algorithm without Computing Global Solutions. Journal of Applied Mathematics No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-993425
American Medical Association (AMA)
Liu, Bingzhuang& Wang, Changyu& Zhao, Wenling. On the Convergence of a Smooth Penalty Algorithm without Computing Global Solutions. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-993425
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993425