New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters

Abstract

Here, three new nonlinear conjugate gradient (NCG) methods are proposed, based on a modified secant equation introduced in (IMA. J. Num. Anal. 11 (1991) 325-332) and optimal Dai-Liao (DL) parameters (Appl. Math. Optim. 43 (2001) 87-101). Firstly, an extended conjugacy condition is obtained, which leads to a new DL parameter. Next, to set this parameter, we use three approaches such that the search directions be close to some descent or quasi-newton directions. Global convergence of the proposed methods for uniformly convex functions and general functions is proved. Numerical experiments are done on a set of test functions of the CUTEr collection and the results of these NCGs are compared with some well-known methods.