An algorithm for the prediction of search trajectory in nonlinear programming problems and optimum design

A simple modification of some methods of mathematical (nonlinear) programming is suggested (Newton's method and the steepest descent method are taken as examples). The modification is made in order to reduce the number of steps for some sequential search methods. The reduction is achieved by extrapolation of the results obtained by the previous search steps. The computation of prognosis points is proposed instead of the large amount of calculation necessary to do the k-th step of the approach process. The extrapolation formulae are obtained by using elements of the random numbers theory. Results of computational tests and solutions of optimum design problems for a frame and a shell demonstrate the efficiency of the proposed method.