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It may happen that <math>-g^{(k)}</math> is not a descent direction for <math>f \ </math> at <math>x^{(k)}</math>. We therefore maintain a list <math>f_{\rm{best}} \ </math> that keeps track of the lowest objective function value found so far, i.e.
:<math>f_{\rm{best}}^{(k)} = \min\{f_{\rm{best}}^{(k-1)} , f(x^{(k)}) \}.</math>
===Step size rules===
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