An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization
type: Item
instance of: scholarly article
title: An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization
zbMATH Open document ID: 1122.65056
author: Detong Zhu
published in: Applied Mathematics and Computation
publication date: 2007-05-14T00:00:00Z
review text: The author presents an affine scaling reduced preconditional conjugate gradient path approach in association with a nonmonotonic interior backtracking line search technique for solving a nonlinear optimization problem subject to both linear equality and linear inequality constraints. Namely, in order to avoid the difficulties of the strictly feasible constraints, the author introduces the affine scaling matrix and reduced Hessian to generate an affine scaling preconditional conjugate gradient path in which the curvilinear path search is used instead of the trust region strategy. Employing the affine scaling preconditional conjugate gradient to form the curvilinear path and using the interior backtracking line search technique, each iterate switches to a trial step for strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of an objective function with large curvature. It is proved that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable smooth conditions.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5152332
zbMATH Keywords: affine scaling
zbMATH Keywords: preconditioner
zbMATH Keywords: interior point
zbMATH Keywords: conjugate gradient
zbMATH Keywords: nonmonotonic interior backtracking line search
zbMATH Keywords: nonlinear optimization
zbMATH Keywords: algorithm
zbMATH Keywords: local superlinear convergence
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: j.amc.2006.05.151
OpenAlex ID: W2063886652
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DOI: 10.1016/J.AMC.2006.05.151
description: scientific article; zbMATH DE number 5152332