Modification of Three-Term Conjugate Gradient Method for Solving Unconstrained Optimization and Image Restoration Problems

Nonlinear conjugate gradient algorithm is highly effective for optimization due to its low storage requirements and simple structure properties. Expanding on the Barzilai and Borwein conjugate gradient method, we propose a three-term conjugate gradient method with a restart procedure for unconstrained optimization. This method ensures global convergence under standard assumptions and employs a standard Wolfe line search. To evaluate its performance, we carry out comprehensive numerical experiments for large scales to address challenges in unconstrained optimization and image restoration. The numerical results prove that the new method is more effective compared to other classical methods.