الملخص

Abstract In this paper, we propose a modified version of the shifted VM algorithms where the matrices have the form where and are symmetric positive semi definite matrices, usually , is obtained from to satisfy the shifted modified quasi-Newton condition ,we consider our new QN-condition the form , where , and we derive of the modified algorithms. Experimental results indicate that the new proposed algorithms were efficient than the both standard BFGS & the shifted BFGS- algorithms.