A superlinearly convergent strongly sub-feasible SSLE-type algorithm with working set for nonlinearly constrained optimization
type: Item
instance of: scholarly article
title: A superlinearly convergent strongly sub-feasible SSLE-type algorithm with working set for nonlinearly constrained optimization
zbMATH Open document ID: 1162.65032
author: Jinbao Jian
author: Weixin Cheng
published in: Journal of Computational and Applied Mathematics
publication date: 2009-03-02T00:00:00Z
review text: The following nonlinear inequality constrained optimization problem is considered: \[ \text{Minimize }f(x)\text{ subject to }g_i(x)\leq 0,\;i=1, \dots, m, \] where \(f:\mathbb{R}^n\to \mathbb{R}\), \(g_i:\mathbb{R}^n\to \mathbb{R}\) for all \(i=1,\dots,m\) are continuously differentiable functions. Using a new identification technique of active constraints and the method of strongly sub-feasible directions, the authors develop a new algorithm based on a sequential system of linear equations. The algorithm can be started from an arbitrary initial point. After a finite number of iterations, the algorithm generates a feasible iteration point and continues its work as the known method of feasible directions. Global, strong and superlinear convergence of the proposed algorithm are proved. Experimental numerical results in the concluding part of the paper show the effectiveness of the algorithm.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C53
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 5522048
zbMATH Keywords: inequality constraints
zbMATH Keywords: nonlinear optimization
zbMATH Keywords: sequential systems of linear equations
zbMATH Keywords: working set
zbMATH Keywords: global and superlinear convergence
describes a project that uses: CUTEr
describes a project that uses: CUTE
MaRDI profile type: Publication
full work available at URL: j.cam.2008.07.017
OpenAlex ID: W2130835075
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DOI: 10.1016/J.CAM.2008.07.017
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description: scientific article; zbMATH DE number 5522048