New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods

Three hybrid methods for solving unconstrained optimization problems are introduced. These methods are defined using proper combinations of the search directions and included parameters in conjugate gradient and quasi-Newton methods. The convergence of proposed methods with the underlying backtracking line search is analyzed for general objective functions and particularly for uniformly convex objective functions. Numerical experiments show the superiority of the proposed methods with respect to some existing methods in view of the Dolan and Moré’s performance profile.