A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function
type: Item
instance of: scholarly article
title: A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function
zbMATH Open document ID: 1148.65045
author: Chun-Ming Tang
author: Jinbao Jian
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-22T00:00:00Z
review text: The authors propose an algorithm for the solution of finite-dimensional, nonlinear, smooth, constrained optimization problems. Therefore a sequential quadratically constrained quadratic programming method is presented which differs from standard sequential quadratic programming (SQP) by using quadratic instead of linear constraints for each subproblem. This approach is a simple extension of the SQP theory used for example by \textit{Y.-H. Dai} and \textit{K. Schittkowski} [Pac. J. Optim. 4, No.~2, 335--351 (2008; Zbl 1154.65046)], the algorithm presented here follows this paper in many details. The augmented Lagrange function used as merit function and also the problem formulation is nearly the same, especially after the final extension from inequality constraints to general constraints and to a nonmonotone linesearch -- apart of course from the added quadratic terms which one has to carry along. Convergence rates are proved to be superlinear and quadratic under certain conditions. No numerical results and hence evidence for superiority of the theory are given so far.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C55
zbMATH DE Number: 5315417
zbMATH Keywords: quadratic constraints
zbMATH Keywords: augmented Lagrangian
zbMATH Keywords: line search
zbMATH Keywords: convergence
zbMATH Keywords: nonlinear programming
reviewed by: M. D. Korzec
describes a project that uses: SOCP
describes a project that uses: NLPQLP
describes a project that uses: NPSOL
MaRDI profile type: Publication
full work available at URL: j.cam.2007.09.024
OpenAlex ID: W2159244544
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DOI: 10.1016/J.CAM.2007.09.024
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description: scientific article; zbMATH DE number 5315417