A penalty-function-free line search SQP method for nonlinear programming
type: Item
instance of: scholarly article
title: A penalty-function-free line search SQP method for nonlinear programming
zbMATH Open document ID: 1169.65060
author: Wenjuan Xue
author: Chungen Shen
author: Dingguo Pu
published in: Journal of Computational and Applied Mathematics
publication date: 2009-05-28T00:00:00Z
review text: The following optimization problem is considered: \[ \text{Minimize }f(x) \text{ subject to }c_i(x)=0,\;i=1,\dots,p,\;c_i(x)\leq 0,\;i=p+1, \dots,m, \] where \(f:\mathbb R^n\to \mathbb R\), \(c_i:\mathbb R^n\to \mathbb R\), \(i=1,\dots,m\) are twice continuously differentiable functions. The authors propose a special sequential quadratic programming (SQP) method for solving the problem. The key point of the concept is that the trial point generated by solving a trust region SQP problem is accepted if there is a sufficient decrease of the objective function or the constraint violation. No penalty parameter needs to be chosen and no filter is used. The proposed method is a non-monotone line search SQP method, which interprets the optimization problem as a bi-objective optimization problem. Local and global convergence of the proposed method is investigated and it is shown that under certain additional conditions the method converges superlinearly. Some numerical results and experiments are reported in the concluding part of the paper.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C55
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5559058
zbMATH Keywords: sequential quadratic programming
zbMATH Keywords: line search
zbMATH Keywords: local convergence
zbMATH Keywords: global convergence
zbMATH Keywords: second order correction
zbMATH Keywords: non-monotonicity
zbMATH Keywords: trust region problem
zbMATH Keywords: numerical results
describes a project that uses: LANCELOT
describes a project that uses: SNOPT
MaRDI profile type: Publication
full work available at URL: j.cam.2008.09.031
OpenAlex ID: W2118309096
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DOI: 10.1016/J.CAM.2008.09.031
description: scientific article; zbMATH DE number 5559058