Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence of memory gradient methods
International Journal of Computer Mathematics
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It is proved that any cluster point of a sequence defined by a steepest descent algorithm in a general normed vector space is a critical point. The function is just assumed to be continuously differentiable. The class of algorithms we consider encompasses several choices such as the Cauchy steplength and the Curry steplength.