In a recent paper, a nonmonotone spectral projected gradient(SPG) method was introduced by Birgin, Martinez and Raydan for the minimization of differentiabie 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 boun-dedness conditions that are assumed in existing results, such as boundedness from below of f, boundedness of X_k or existence of accumulation point of {x_k}. 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 itetates generated by this method and the finite termination etc. Therefore, these results show that the SPG method is attractive in theory.
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