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Two descent hybrid conjugate gradient methods for optimization. (English) Zbl 1142.65050
The aim of the paper is to study convergence and computational properties of two new descent hybrid conjugate gradient methods for nonlinear optimization problems consisting in the global minimization of a continuously differentiable function of $n$ variables over ${ℝ}^{n}$. The methods require no restarts and produce a sufficient descent search direction in each iteration. No convexity assumptions are required. The obtained results hold for functions with bounded level sets and bounded Lipschitz continuous gradients. The numerical results presented at the end of the paper show a good efficiency of the proposed methods.
##### MSC:
 65K05 Mathematical programming (numerical methods) 90C30 Nonlinear programming