Derivative-free HS-DY-type method for solving nonlinear equations and image restoration.

A derivative-free conjugate gradient algorithm for solving nonlinear equations and image restoration is proposed. The conjugate gradient (CG) parameter of the proposed algorithm is a convex combination of Hestenes-Stiefel (HS) and Dai-Yuan (DY) type CG parameters. The search direction is descent and bounded. Under suitable assumptions, the convergence of the proposed hybrid algorithm is obtained. Using some benchmark test problems, the proposed algorithm is shown to be efficient compared with existing algorithms. In addition, the proposed algorithm is effectively applied to solve image restoration problems.