An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

Abstract

Motivated by the projection technique, in this paper, we introduce a new method for approximating the solution of nonlinear equations with convex constraints. Under the assumption that the associated mapping is Lipchitz continuous and satisfies a weaker assumption of monotonicity, we establish the global convergence of the sequence generated by the proposed algorithm. Applications and numerical example are presented to illustrate the performance of the proposed method.

Keywords

• unconstrained optimization
• nonlinear equations
• convex constrained
• conjugate gradient method
• projection method
• compressive sensing