Solving Large-Scale Unconstrained Optimization Problems with an Efficient Conjugate Gradient Class

The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems. The presented class enjoys the benefits of having three free parameters, its directions are descent, and it can fulfill the Dai–Liao conjugacy condition. Global convergence property of the new class is proved under the weak-Wolfe–Powell line search technique. Numerical efficiency of the proposed class is confirmed in three sets of experiments including 210 test problems and 11 disparate conjugate gradient methods.