A conjugate gradient algorithm based on double parameter scaled Broyden–Fletcher–Goldfarb–Shanno update for optimization problems and image restoration

In this paper, we present a three-term conjugate gradient algorithm and three approaches are used in the designed algorithm: (i) A modified weak Wolfe-Powell line search technique is introduced to obtain $$\alpha _k$$ . (ii) The search direction $$d_k$$ is given by a symmetrical Perry matrix which contains two positive parameters, and the sufficient descent property of the generated directions holds independent of the MWWP line search technique. (iii) A parabolic will be proposed and regarded as the projection surface, the next point $$x_{k+1}$$ is generated by a new projection technique. The global convergence of the new algorithm under a MWWP line search is obtained for general functions. Numerical experiments show that the given algorithm is promising.