Spectral three-term conjugate descent method for solving nonlinear monotone equations with convex constraints

Auwal Bala Abubakar, Jewaidu Rilwan, Seifu Endris Yimer, Abdulkarim Hassan Ibrahim, Idris Ahmed

Abstract

This paper proposes three (3) three term conjugate gradient (CG) methods based on the well known conjugate descent (CD) CG parameter. The two directions were obtained by adding a term to the CD direction such that the sufficient descent property is satisfied. Under some assumptions, we establish the convergence of the proposed methods. In addition, numerical examples were given to show the capability of the two methods in solving nonlinear monotone equations with convex constraints.