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.
Nezhadhosein, S. (2020). New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters. Journal of Mathematical Modeling, 8(1), 21-39. doi: 10.22124/jmm.2019.14737.1338
MLA
Saeed Nezhadhosein. "New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters". Journal of Mathematical Modeling, 8, 1, 2020, 21-39. doi: 10.22124/jmm.2019.14737.1338
HARVARD
Nezhadhosein, S. (2020). 'New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters', Journal of Mathematical Modeling, 8(1), pp. 21-39. doi: 10.22124/jmm.2019.14737.1338
VANCOUVER
Nezhadhosein, S. New nonlinear conjugate gradient methods based on optimal Dai-Liao parameters. Journal of Mathematical Modeling, 2020; 8(1): 21-39. doi: 10.22124/jmm.2019.14737.1338
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