A hybrid approach for finding approximate solutions to constrained nonlinear monotone operator equations with applications

In this article, a hybrid approach technique incorporated with three term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is defined such that it is close to the one obtained by the memory-less Broyden-Fletcher-Goldferb-Shanno (BFGS) method. Independent of the line search, the search direction possesses the sufficient descent and trust region properties. Furthermore, the sequence of iterates generated converge globally under some appropriate assumptions. In addition, numerical experiments are carried out to test the efficiency of the proposed method in contrast with existing methods. Finally, the applicability of the proposed method in compressive sensing is shown. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.