A hybrid three-term conjugate gradient projection method with the general acceleration for nonlinear equations

Abstract In this paper, we propose a hybrid three-term conjugate gradient projection method with the general acceleration for solving nonlinear equations. The acceleration parameter encompasses the convex combination parameter, the inertial parameter, and their hybridization. The search direction designed has good theoretical properties independent of line searches. Without the Lipschitz continuity of the underlying mapping, we establish the global convergence of the proposed algorithm. Importantly, we demonstrate the local convergence rate of the proposed algorithm under the locally Lipschitz continuity condition. Finally, solving benchmark test instances and sparse signal recovery problems demonstrates the effectiveness and robustness of the proposed algorithm. Mathematics Subject Classification (2010) 65K10 · 90C56