An efficient three-term conjugate gradient algorithm with restart strategy and image restoration

In this paper, a new effective hybrid three-term conjugate gradient method with restart procedure is proposed to solve unconstrained optimizations. We propose a novel search direction that approximates the memoryless BFGS quasi-Newton direction, forming a hybrid structure derived from FR, CD, and DY conjugate parameters, which demonstrates excellent performance in large-scale problems. Its sufficient descent property is demonstrated. Under certain assumptions and the weak Wolfe line search conditions, the global convergence is analyzed. Two sets of numerical experiments on 100 test functions are conducted to evaluate the proposed algorithm. Numerical experiments show that it outperforms some other conjugate gradient algorithms. Furthermore, the proposed algorithm demonstrates superior performance in image restoration, achieving higher peak signal-to-noise ratio values.