Alternative Algorithms of Broyden FAMILYAMI: for Unconstrained Optimization

The Broyden family method for unconstrained optimization is known as one of the most efficient method in solving unconstrained optimization problem. Step size and search direction play the most important role to the convergence of the Broyden family method. Step size is proved to be successful method to solve the problem; however, it is definite to solve some complicated optimization problems. In this paper, we introduced the alternative procedure in determining the step size. This alternative procedure will be applied in the hybrid Broyden method. The numerical results based on number of iterations, number of gradient evaluation and number of function evaluation are given at the end of the paper.