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Conjugate gradient (CG) methods are a popular family of iterative algorithms to solve large-scale nonlinear optimization problems due to appropriate features such as no need to calculate the second-order derivatives, low storage and computation, and suitable convergence rate. In this paper, based on the Hestenes-Stiefel method and Conjugate Descent method, new hybrid conjugate gradient method (named hHC method) is proposed for unconstrained optimization. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical tests demonstrate the effectiveness of the new hybrid conjugate gradient method when compared to certain existing methods in view of the Dolan and Moré performance profile. Furthermore, the proposed algorithm was extended to solve problem of mode function.
Chaib et al. (Tue,) studied this question.