A modified Hestenes–Stiefel projection method for constrained nonlinear equations and its linear convergence rate

Abstract

The Hestenes–Stiefel (HS) method is an efficient method for solving large-scale unconstrained optimization problems. In this paper, we extend the HS method to solve constrained nonlinear equations, and propose a modified HS projection method, which combines the modified HS method proposed by Zhang et al. with the projection method developed by Solodov and Svaiter. Under some mild assumptions, we show that the new method is globally convergent with an Armijo line search. Moreover, the R-linear convergence rate of the new method is established. Some preliminary numerical results show that the new method is efficient even for large-scale constrained nonlinear equations.