A new hybrid three-term HS-DY conjugate gradient in solving unconstrained optimization problems

Conjugate Gradient (CG) method is an interesting tool to solve optimization problems in many fields, such design, economics, physics and engineering. Until now, many CG methods have been developed to improve computational performance and have applied in the real-world problems. Combining two CG parameters with distinct denominators may result in non-optimal outcomes and congestion.In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The hybrid three-term search direction combines Hestenes-Stiefel (HS) and Dai-Yuan (DY) CG parameters which standardized by using a spectral to determine the suitable conjugate parameter choice and satisfies the sufficient descent condition. Additionally, the global convergence was proved under standard Wolfe conditions and some suitable assumptions. Furthermore, the numerical experiments showed the proposed method is most robust and superior efficiency compared to some existing methods.

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