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A very fast nongradient procedure for function optimization is described. The procedure is based on the ideas of Rosenbrock  and Swann . These were modified and refined to obtain an algorithm which provides an optimum with a very small number of function evaluations. This algorithm, compared with recently reported algorithms by Lawrence and Steglitz (L-S) , and Beltrami and Indusi (B-I) , appears to be very robust and reliable. Constrained optimization problems can be handled and a special method for handling optimization with linear constraints is presented.