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In this paper, a derivative-free Hestenes–Stielfel type method is proposed to solve large-scale nonlinear equations with convex constraints. The proposed method adopts the line search proposed by Ou and Li [J. Comput. Appl. Math. 56(1-2) (2018), pp. 195–216]. Unlike most existing methods, the global convergence of the proposed method is established under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Preliminary numerical experiments indicate that the proposed method is effective and promising. Furthermore, the proposed method is used to solve image restoration problem in compressive sensing.

A derivative-free three-term Hestenes–Stiefel type method for constrained nonlinear equations and image restoration