An adaptive Barzilai and Borwein projection method for nonlinear equations

Abstract

The Barzilai and Borwein methods are renowned for their simplicity and numerical efficiency, attracting significant attention for large-scale optimization problems. Recently, a new adaptive Barzilai and Borwein method with a nonmonotone line search has been proposed for general unconstrained optimization. Building on this approach, we propose, analyze and test an adaptive Barzilai and Borwein method to solve systems of nonlinear equations with convex constraints, incorporating a hyperplane projection technique. The proposed method has several attractive properties, including not requiring Jacobian information and avoiding matrix storage per iteration. Under standard assumptions, the global convergence of the proposed method is established. Finally, numerical experiments are presented to demonstrate the practical performance of the proposed method.