THE MINIMIZATION of a unimodal function of a single variable, specified in an unbounded set, is considered. The efficiencies of algorithm giving localization of the minimum in the intial unbounded set are estimated numerically, and the optimal algorithm is found. The algorithm makes essential use of the standard method of Fibonacci numbers and can be regarded as a generalization of the latter. A similar treatment is given of the having method as applied to localization of the point where a one-dimensional function changes sign, when this point is known to be unique but the interval in which it lies is unknown.