α-PSB update method

Abstract

Abstract In this work, we propose modification for PSB update with a new extended Quasi – Newton condition for unconstrained optimization problem, so it’s called (α – PSB) method. PSB update kind of rank two update, which solve the unconstrained optimization problem, but this update can’t guarantee the positive definite property of Hessian matrix. In this work, the guarantee of positive definite property for the Hessian matrix be confirmed by updating the vector sk, which represent the difference between the next gradient and the current gradient of the objective function which assume to be continuous twice and differentiable. Then we proved the existentialism of this update. Numerical results are reported where the comparison between the proposed method and the PSB update method under standard problems.