Descent three-term DY-type conjugate gradient methods for constrained monotone equations with application

As it is known that, not all conjugate gradient (CG) methods satisfy descent property, a necessary condition for attaining global convergence result. In this article, we propose three different sufficient-descent conjugate gradient projection algorithms for constrained monotone equations. Using Dai–Yuan (DY) conjugate gradient parameter, we generate three satisfied sufficient-descent directions. Under suitable conditions, global convergence of the algorithms is established. Numerical examples using benchmark test functions indicate that the algorithms are effective for solving constrained monotone nonlinear equations. Moreover, we also extend the method to solve ℓ 1 -norm regularized problems to decode a sparse signal in compressive sensing. Performance comparisons show that the proposed methods are practical, efficient and competitive with the compared methods.