A Mixed Non-monotone Direct Search Conjugate Gradient Method

摘要

Direct search method is an important method for optimization problems especially when the gradient information of the objective function is not available or computational expensively. In direct search method, sufficient decrease condition is often needed to achieve convergence and search outside the grid defined by positive bases. In this paper, nonmonotone decrease condition is employed together with the sufficient decrease condition. Such a mixed non-monotone strategy is used in Coope-Price’s direct search framework. A preconditioned PRP+ conjugate gradient is also employed in this framework to accelerate convergence. Global convergence is shown for such a mixed non-monotone direct search conjugate gradient method. Numerical experiments show that the mixed non-monotone strategy improves the numerical performance greatly and the mixed non-monotone direct search conjugate gradient method is effective.