Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
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There are two procedures for applying the method of conjugate gradients to the problem of minimizing a convex, nonlinear function: the "continued" method, and the "restarted" method in which all the data except the best previous point are discarded, and the procedure is begun a new from that point. It is demonstrated by example that in the absence of the standard initial starting condition on a quadratic function, the continued conjugate gradient method will converge to the solution no better than linearly. Furthermore, it is shown that for a general nonlinear function, the nonrestarted conjugate gradient method converges no worse than linearly.