Of all the computations required for a typical descent method, that of the step length might appear to be the simplest. Unfortunately this is not the case since it is important to obtain a new point F(x ) which is (k) sufficiently lower than the current point F(x ) for overall convergence (k) of the descent method to be guaranteed. Often an algorithm requires a (k) to minimize F(x) along the vector p. Our experience is chat exact univariate minimization is almost as difficult as its multi-dimensional counterpart. An inadequate choice of step will either give slow convergence or cause the algorithm to fail completely.
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