期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 405, 期 1, 页码 310-319出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2013.04.017
关键词
Unconstrained optimization; Monotone equations; Conjugate gradient method; Projection method; Compressive sensing
资金
- NSF of China [NSFC-11001075]
- Natural Science Foundation of Henan Province [122300410385]
CG_DESCENT is a state-of-the-art algorithm to solve large-scale unconstrained minimization problems. However, research activities on CG_DESCENT in some other scenarios are relatively fewer. In this paper, by combining with the projection method of Solodov and Svaiter, we extend CG_DESCENT to solve large-scale nonlinear convex constrained monotone equations. The proposed method does not require the Jacobian information, even though it does not store any matrix at each iteration. It thus has the potential to solve large-scale non-smooth problems. Under some mild conditions, we show that the proposed method converges globally. Primary numerical results illustrate that the proposed method works quite well. Moreover, we also extend this method to solve the l(1)-norm regularized problems to decode a sparse signal in compressive sensing. Performance comparisons show that the proposed method is practical, efficient and competitive with the compared ones. (C) 2013 Elsevier Inc. All rights reserved.
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