Step lengths in BFGS method for monotone gradients

In this paper, we consider how to directly apply the BFGS method to finding a zero point of any given monotone gradient and thus suggest new conditions to locate the corresponding step lengths. The suggested conditions involve curvature condition and merely use gradients' computations. Furthermore, they can guarantee convergence without any other restrictions. Finally, preliminary numerical experiments indicate their practical effectiveness in solving some systems of nonlinear equations arising in boundary value problems and others.

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