Two extensions of the Dai-Liao method with sufficient descent property based on a penalization scheme

To achieve the good features of the linear conjugate gradient algorithm in a recent extension of the Dai-Liao method, two adaptive choices for parameter of the extended method are proposed based on a penalization approach. It is shown that the suggested parameters guarantee the sufficient descent property independent to the line search and the objective function convexity. Furthermore, they ensure the global convergence of the related algorithm for uniformly convex objective functions. Using a set of unconstrained optimization test problems from the CUTEr library, effectiveness of the suggested choices are numerically compared with two other recently proposed adaptive choices. Results of comparisons show that one of the proposed choices is computationally promising in the sense of the Dolan-Moré performance profile.