Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24557
Title: Convergence properties of nonmonotone spectral projected gradient methods
Authors: Wang, C
Liu, Q
Yang, X
Keywords: Nonmonotone linear search
Convergence
Finite termination
Issue Date: 2005
Publisher: North-Holland
Source: Journal of computational and applied mathematics, 2005, v. 182, no. 1, p. 51-66 How to cite?
Journal: Journal of computational and applied mathematics 
Abstract: In a recent paper, a nonmonotone spectral projected gradient (SPG) method was introduced by Birgin et al. for the minimization of differentiable functions on closed convex sets and extensive presented results showed that this method was very efficient. In this paper, we give a more comprehensive theoretical analysis of the SPG method. In doing so, we remove various boundedness conditions that are assumed in existing results, such as boundedness from below of f, boundedness of xk or existence of accumulation point of {xk}. If ∇f(·) is uniformly continuous, we establish the convergence theory of this method and prove that the SPG method forces the sequence of projected gradients to zero. Moreover, we show under appropriate conditions that the SPG method has some encouraging convergence properties, such as the global convergence of the sequence of iterates generated by this method and the finite termination, etc. Therefore, these results show that the SPG method is attractive in theory.
URI: http://hdl.handle.net/10397/24557
ISSN: 0377-0427
EISSN: 1879-1778
DOI: 10.1016/j.cam.2004.10.018
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