Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization

Several attempts have been made to modify the quasi-Newton condition in order obtain rapid convergence with complete properties (symmetric and positive definite) of inverse Hessian matrix (second derivative objective function). There are many unconstrained optimization methods that do not generate definiteness matrix. One those is symmetric rank 1( H-version) update (SR1 update), where this satisfies property matrix, but does preserve definite initial definiteness. The for very important guarantee existence minimum point function determine value function.