On the convergence of a smooth penalty algorithm without computing global solutions
type: Item
instance of: scholarly article
title: On the convergence of a smooth penalty algorithm without computing global solutions
zbMATH Open document ID: 1235.90120
DOI: 10.1155/2012/620949
author: Bingzhuang Liu
author: Changyu Wang
author: Wenling Zhao
published in: Journal of Applied Mathematics
publication date: 2012-04-04T00:00:00Z
review text: Summary: 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 problems.
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 6021719
Wikidata QID: Q58906254
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/620949
OpenAlex ID: W2051191129
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description: scientific article; zbMATH DE number 6021719