A Globally Convergent Spectral Three-Term Conjugate Gradient Method With Applications to 4DOF Robotic Trajectory Tracking

This paper proposes a new spectral three-term conjugate gradient (STTCG) method for solving large-scale unconstrained optimization problems. The proposed method integrates the Liu–Storey conjugate gradient parameter with a modified three-term correction and a safeguarded Barzilai–Borwein spectral scaling strategy to enhance both robustness and computational efficiency. The resulting search direction satisfies the sufficient descent condition independently of the line search procedure, while its conjugacy property is established under a positive curvature condition. Furthermore, the global convergence of the proposed method is proved under standard assumptions. Extensive numerical experiments on 120 benchmark test problems with dimensions ranging from n=2 to n=500,000 demonstrate that STTCG is competitive with five state-of-the-art conjugate gradient methods in terms of the number of iterations, function evaluations, and CPU time. To further demonstrate its practical applicability, the proposed method is employed in the trajectory tracking of a four-degrees-of-freedom (4DOF) robotic manipulator, where it exhibits accurate tracking performance and favorable computational efficiency.MSC2020 Classfication: 65K05 | 90C52 | 90C56 | 94A08