About The Convergence Of The Optimization Method

This paper mainly studies some convergences for optimization methods. The first part gives a simpler proof of global convergence of Broyden class Quasi-Newton method with inexact line search. This proof is simpler than that given in [1]. In fact, it generalizes and modifies the proof of the global convergence of BFGS method in [3]. At the second part, nonmonotonic trust region method for unconstrained optimization is studied. This method allows an increase in the objective function value at some step, while retaining global convergence. Finally, numerical expriments show that the nonmonotonic trust region method is superior to the usual trust region methods.