A modified SLP algorithm and its global convergence

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• 作者：Aiqun Huang^a ; ^{huangaiqun776@yahoo.com.cn"" rel=""nofollow} ; Chengxian Xu^b ; ^{mxxu@mail.xjtu.edu.cn"" rel=""nofollow} ; Meihua Wang^b ; ^{yuyu0504@163.com"" rel=""nofollow}
• 关键词：Nonlinear programming ; Global convergence ; Filter ; SLP
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2011
• 出版时间：15 May 2011
• 年：2011
• 卷：235
• 期：14
• 页码：4302-4307
• 全文大小：210 K

文摘

This paper concerns a filter technique and its application to the trust region method for nonlinear programming (NLP) problems. We used our filter trust region algorithm to solve NLP problems with equality and inequality constraints, instead of solving NLP problems with just inequality constraints, as was introduced by Fletcher et al. [R. Fletcher, S. Leyffer, Ph.L. Toint, On the global converge of an SLP-filter algorithm, Report NA/183, Department of Mathematics, Dundee University, Dundee, Scotland, 1999]. We incorporate this filter technique into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the tradition trust region method, our algorithm performs a nonmonotone filter technique to find a new iteration point if a trial step is not accepted. Under mild conditions, we prove that the algorithm is globally convergent.