A modified four-term extension of the dai-liao conjugate gradient method

. In this paper, a modified Dai-Liao type four-term conjugate gradient method is proposed. Based on the estimation of the Rayleigh quotient of the iteration matrix of search direction, choices for the parameter mentioned above self-adjust the weight between the sufficient descent condition and reduction in the condition number of iteration matrix of the search direction, which can be regarded as inheritance and development of the originally optimal choices for a set of parameters t*& theta;k (JIMO,13(2):649-658,2017). Meanwhile, sufficient descent condition of the modified search direction is satisfied at each iteration. Under mild conditions, global convergence of the resulting method are established even if the objective function is nonconvex. Some comparative numerical results illustrate the efficiency of the proposed method.