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This book is concerned with modifications and developments of minimization methods for nonlinear unconstrained optimization problems with the objective of improving the efficiency of these method at high dimensions. The derivation of new spectral CG method depends on the quadratic function, conjugacy and secant conditions to modified the Dai-Yuan method. Also, we investigated two new kinds conjugacy coefficient which do not only contain gradient value information, but also function value information at present and previous step. By using the idea of memoryless BFGS quasi-Newton type method with Hager and Zhang formula to obtain three terms CG. Finally, the training multilayer feed forward networks was used to train two methods (MDY & three terms HZ).