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

Here, three new nonlinear conjugate gradient (NCG) methods are proposed,  based on a modified secant equation introduced in (IMA. J.  Num.  Anal. ۱۱ (۱۹۹۱) ۳۲۵-۳۳۲) and optimal Dai-Liao (DL) parameters (Appl.  Math.  Optim.  ۴۳ (۲۰۰۱) ۸۷-۱۰۱). 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.

کلیدواژه ها:

Unconstrained optimization ، Modified secant equations ، Dai-Liao conjugate gradient method