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Abstract and Applied Analysis
Volume 2014, Article ID 236158, 9 pages
Research Article

Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Algorithm for Large-Scale Box-Constrained Optimization

1College of Software, Henan University, Kaifeng 475000, China
2College of Mathematics and Information Science, Henan University, Kaifeng 475000, China

Received 7 December 2013; Accepted 14 February 2014; Published 13 April 2014

Academic Editor: Gaohang Yu

Copyright © 2014 Qiuyu Wang and Yingtao Che. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A practical algorithm for solving large-scale box-constrained optimization problems is developed, analyzed, and tested. In the proposed algorithm, an identification strategy is involved to estimate the active set at per-iteration. The components of inactive variables are determined by the steepest descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method—L-BFGS-B.