An efficient hybrid three-term conjugate gradient method with practical applications

The conjugate gradient method is widely used for large-scale unconstrained optimization due to its efficiency in iteration number and computing time. In this paper, we present a new parameter βₖ by hybridizing the Liu-Storey parameter βₖLS and its modification βₖDLS. We also use a hybrid three-term technique ensuring sufficient descent based on strong Wolfe conditions. We prove that the new direction possesses the descent property and that the corresponding algorithm is globally convergent. Numerical experiments on test problems and some applications, such as image restoration and sparse signal recovery, further show that our approach is efficient, consistently outperforming other approaches in terms of convergence speed and solution quality.