An augmented memoryless Davidon–Fletcher–Powell method based on the Dai–Liao approach

Abstract

ABSTRACT For the sake of enhancing computational efficiency of the memoryless Davidon–Fletcher–Powell method, we set a direct link between this method and the Dai–Liao technique. Thus, we make it possible to organize assistance for the memoryless Davidon–Fletcher–Powell method from the numerical viewpoint, in the framework of a two-parameter algorithm. One of the parameters of the method is determined based on a modified secant equation while the other can benefit from the classic adaptive formulas of the Dai–Liao parameter. We discuss when the sufficient descent condition holds and how it can serve for the convergence of the method. Then, we review some smoothing plans for a classic nonsmooth minimization model which frequently appears in the real-world applications. Ultimately, we perform computational tests to mirror the efficiency of the method and then, we report the results as well.