Modified shifted variable metric algorithms for solving unconstrained minimization problems

Abstract EN

In this paper, we propose a modified version of the shifted VM algorithms where the matrices k H have the form , k k k H = ξ I + A 1 ≥ k where 0 f k ξ and k A are symmetric positive semi definite matrices, usually 0 1 A = , k +1 A is obtained from k A to satisfy the shifted modified quasi-Newton condition ,we consider our new QN-condition the form , ~ * * k 1 k k k A y = ρ v + * ~ k k k k v = v −ξ y , k k k k y* = y + m v where * * * / *k T k k k T k k ρ = y A y v y , 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.