A New Dai-Liao Conjugate Gradient Method with Optimal Parameter Choice

A new nonlinear conjugate gradient method is proposed to solve large-scale unconstrained optimization problems. The direction is given by a search direction matrix, which contains a positive parameter. The value of the parameter is calculated by minimizing the upper bound of spectral condition number of the matrix defining it in order to cluster all the singular values. The new search direction satisfies the sufficient descent condition. Under some mild assumptions, the global convergence of the proposed method is proved for uniformly convex functions and the general functions. Numerical experiments show that, for the CUTEr library and the test problem collection given by Andrei, the proposed method is superior to M1 proposed by Babaie-Kafaki and Ghanbari (Eur. J. Oper. Res. 234(3), 625–630, 2014), CG_DESCENT(5.3), and CGOPT.