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Inexact spectral projected gradient methods on convex sets

Inexact spectral projected gradient methods on convex sets A new method is introduced for large‐scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented using inexact projections computed by Dykstra's alternating projection method and generates interior iterates. The ISPG method is a generalization of the Spectral Projected Gradient method (SPG), but can be used when projections are difficult to compute. Numerical results for constrained least‐squares rectangular matrix problems are presented. Key words http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png IMA Journal of Numerical Analysis Oxford University Press

Inexact spectral projected gradient methods on convex sets

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References (31)

Publisher
Oxford University Press
Copyright
Copyright © 2015 Institute of Mathematics and its Applications
ISSN
0272-4979
eISSN
1464-3642
DOI
10.1093/imanum/23.4.539
Publisher site
See Article on Publisher Site

Abstract

A new method is introduced for large‐scale convex constrained optimization. The general model algorithm involves, at each iteration, the approximate minimization of a convex quadratic on the feasible set of the original problem and global convergence is obtained by means of nonmonotone line searches. A specific algorithm, the Inexact Spectral Projected Gradient method (ISPG), is implemented using inexact projections computed by Dykstra's alternating projection method and generates interior iterates. The ISPG method is a generalization of the Spectral Projected Gradient method (SPG), but can be used when projections are difficult to compute. Numerical results for constrained least‐squares rectangular matrix problems are presented. Key words

Journal

IMA Journal of Numerical AnalysisOxford University Press

Published: Oct 1, 2003

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