A new combining algorithm and its global convergence for unconstraint optimization problem

Abstract EN

In this paper, an algorithm for solving nonlinear unconstrained optimization problem by combining extended Conjugate Gradient (CG) and the damped-technique of Powell for the BFGS method to the Broyden family of quasi-Newton method is proposed .

The basic idea is to choose a combination of the damped-technique of Powell and some pervious search directions using inexact line search as new search direction.

We show that the global convergence for the new methods is possible and present, in particular.

The global convergence property of the new algorithm is investigated under few weak conditions.