In the minimization of real valued functions, Newton's algorithm is often combined with a line search method. Grippo et al [SIAM J. Numer. Anal., Vol. 23, No. 4 ] first suggested a nonmonotone stepsize selection rule based on the maximum of a fixed set of previous function values. In this paper we introduce the notion of relaxing functions and suggest several other nonmonotone procedures using a modified Newton direction. Computational performance on several standard test problems is presented,

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... which shows that the proposed models are viable alternatives.