An Alternative Three-Term Conjugate Gradient Algorithm for Systems of Nonlinear Equations

Abstract. This paper presents an alternative three-term conjugate gradient algorithm for solving large-scale systems of nonlinear equations. The proposed method is the modication of memoryless BFGS quasi-Newton update for which the direction is descent using projection based technique together with Powel restarting criteria. Moreover, we proved the global con- vergence of the proposed method with a derivative free line search under suitable assumptions. The numerical results show that the proposed method is promising.