A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

Comment on “A new three-term conjugate gradient method for unconstrained problem”

“…The search direction, which was obtained by symmetrization of the iteration matrix Q k corresponding to the solution of the quadratic model minimization, and satisfied the Dai-Liao conjugacy condition and sufficient descent condition. The CG methods with sufficient descent property and adaptive conjugacy condition have been developed by Babaie-Kafaki and Reza [2], Narushima et al [3], Sugiki et al [4], Andrei [5,6] and Dong et al [7][8][9]. In [1], in order to obtain an optimal parameter ω, a minimization of the condition number of the iteration matrix is discussed.…”

A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems

“…If the Armijo line search is used, using the line search rule, if ̸ = 1, then = −1 will not satisfy line search condition (12). Namely,…”

“…The PRP algorithm [6,7] is one of the most effective CG algorithms and its convergence can be found (see [7,9,10], etc.). Powell [9] suggested that should not be less than zero; then many new CG formulas are proposed (see [11][12][13][14][15][16][17], etc.) to ensure the scalar ≥ 0.…”

A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

“…These were the first scalars β k for nonlinear conjugate gradient methods to be proposed. Since then, other parameters β k have been proposed in the literature (see for example [1,2,[4][5][6]14,15,17,19,22,28,35,39,40] and references therein). From the literature, it is well known that FR and DY methods have strong convergence properties.…”