New Convex Combination (H-version) method for unconstrained optimization problem

Abstract

In this essay, we propose a new family for inverse of Hessian matrix  which based on definition of   convex combination class and on modified symmetric rank one update (MSR1) with (DFP) update and upgraded BFGS (MBFGS) revision for the inverse of the Hessian matrix and the properties of symmetric and positive definite will be shown  and proved as well as the theoretical and numerical  global converge is proposed  , numerical experiment on eight functions are presented in a table.