α-PSB update method

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