Two Settings of the Dai-Liao Parameter Based on Modified Secant Equations

Abstract

Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hestenes-Stiefel CG method‎. ‎The second is based on the quasi-Newton (QN) approach‎. ‎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 are compared with some well-known methods.