A descent scaled conjugate gradient method for unconstrained optimization with its applications in image restoration problems

Based on combining the conjugate gradient method proposed by Hager and Zhang with the scaled gradient idea, we presented a new scaled conjugate gradient method which satisfies the sufficient descent condition. In our method, the scaled parameter is determined so that the search direction becomes close to the three-term HS method suggested by Zhang, Zhou and Li. It is proved that the new method is globally convergent for general nonlinear functions, under some standard assumptions. Numerical comparisons on some test problems from the CUTEst library and image restoration problems illustrate the efficiency and robustness of our proposed method in practice.