Inertial Derivative-Free Projection Method for Nonlinear Monotone Operator Equations With Convex Constraints

Abstract

In this paper, we propose an inertial derivative-free projection method for solving convex constrained nonlinear monotone operator equations (CNME). The method incorporates the inertial step with an existing method called derivative-free projection (DFPI) method for solving CNME. The reason is to improve the convergence speed of DFPI as it has been shown and reported in several works that indeed the inertial step can speed up convergence. The global convergence of the proposed method is proved under some mild assumptions. Finally, numerical results reported clearly show that the proposed method is more efficient than the DFPI.

Keywords

• Monotone nonlinear operator
• inertial algorithm
• conjugate gradient
• projection method