Modified shifted variable metric algorithms for solving unconstrained minimization problems

In this paper, we propose a modified version of the shifted VM algorithms where the matrices k H have the form , k k k A I H + = ξ 1 ≥ k where 0 f k ξ and k A are symmetric positive semi definite matrices, usually 0 1 = A , 1 + k A is obtained from k A to satisfy the shifted modified quasi-Newton condition ,we consider our new QN-condition the form , ~ * * 1 k k k k v y A ρ = + * ~ k k k k y v v ξ − = , k k k k v m y y + = * where / k T k k k T k k y v y A y = ρ , and we derive of the modified algorithms. Experimental results indicate that the new proposed algorithms were efficient than the both standard BFGS & the shifted BFGSalgorithms. Modified shifted variable metric algorithms for solving unconstrained ... ٧١