New Variable Metric Algorithm by The Mean of 2nd Order Quasi-Newton Condition

In this paper a new class of Quasi-Newton update for solving unconstrained nonlinear optimization problem is proposed. In this work we suggested a new formula for the variable metric update with a new quasi-Newton condition used for the symmetric rank two formula.
Finally, a numerical study is reported in which the performance of this new algorithm is compared to that of various members of the unmodified family. Numerical experiments indicate that this new algorithm is effective and superior to the standard BFGS and DFP algorithms, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).