An SQP algorithm with cautious updating criteria for nonlinear degenerate problems
type: Item
instance of: scholarly article
title: An SQP algorithm with cautious updating criteria for nonlinear degenerate problems
zbMATH Open document ID: 1180.65078
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2009-11-13T00:00:00Z
review text: An efficient sequential quadratic programming (SQP) algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the exact penalty function through an Armijo-type line search scheme. This SQP algorithm with cautious update criteria can be considered as a modification of the SQP algorithm given by \textit{J. F. A. de O. Pantoja} and \textit{D. Q. Mayne} [J. Optimization Theory Appl. 69, No. 3, 441--467 (1991; Zbl 0724.90065)]. In the algorithm, the form of quadratic programming subproblem is slightly different from the one given in [loc. cit.], and the update way for the penalty parameter of the used merit function is also different from the usual ways. The global convergence of the algorithm is obtained under the condition of the generalized Mangasarian-Fromvitz constraint qualification. Compared with the previous work [loc. cit.], the boundedness of the solution to the subproblem and the secon-order sufficient condition are not needed. In particular, the algorithm does not need an extra calculation when the iterate point is infesible, which is necessary in the algorithm proposed by \textit{J. Zhang} and \textit{X. Zhang} [Acta Math. Appl. Sin., Engl. Ser. 18, No. 1, 77--84 (2002; Zbl 1114.90480)]. Numerical results indicate that the algorithm is efficient.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C55
zbMATH DE Number: 5632888
zbMATH Keywords: degenerate problem
zbMATH Keywords: exact penalty function
zbMATH Keywords: algorithm
zbMATH Keywords: cautious update criteria
zbMATH Keywords: global convergence
zbMATH Keywords: nonlinear programming
zbMATH Keywords: sequential quadratic programming
author: Taowen Liu
author: Jinping Zeng
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: s10255-004-4100-0
OpenAlex ID: W2039903754
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DOI: 10.1007/S10255-004-4100-0
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description: scientific article; zbMATH DE number 5632888