A new conjugate gradient method with a restart direction and its application in image restoration

We established a new conjugate gradient method with an efficient restart direction for solving large scale unconstrained optimization problems. The modified method was proposed under the Polak-Ribie`re-Polyak conjugate gradient method. Under the strong Wolfe line search, the search direction of the new method was sufficiently descent and its global convergence property could be proved. Compared with other methods having good numerical performances, numerical experiments and image restorations showed that the modified method was more effective.