A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration

The conjugate gradient is a useful tool in solving large- and small-scale unconstrained optimization problems. In addition, the method can be applied many fields, such as engineering, medical research, computer science. this paper, convex combination of two different search directions proposed. new satisfies sufficient descent condition convergence analysis. Moreover, formula properties with property related to Hestenes–Stiefel formula. numerical results show that direction outperforms both directions, making it between them. result includes number iterations, function evaluations, central processing unit time. Finally, we present some examples about image restoration an application proposed method.