الملخص

Two new hybrid algorithms have been suggested in this paper, the first one utilizes four formula of self-scaling update matrix was used. The matrix is selected according to Buckley method in each step. The new algorithm has been compared with BFGS standard algorithm by means of (10) multi-dimensional standard functions. As for the second new hybrid algorithm, a new method is used to test the conjugate coefficient (β) which consists of Hestenes Stiefel (HS) and Dai and yuan (DY). Then it is compared with BFGS and PCG algorithms, which uses BFGS update, by means of (10) multi-dimesional standard functions.             Numerical results in general indicates the efficiency of the algorithms proposed in this paper by using this number of non-linear functions in this domain.