A new inertial-based method for solving pseudomonotone operator equations with application

Many efforts have been made to develop efficient algorithms for solving system of nonlinear equations due to their applications in different branches of science. Some of the classical techniques such as Newton and quasi-Newton methods involve computing Jacobian matrix or an approximation to it at every iteration, which affects their adequacy to handle large scale problems. Recently, derivative-free algorithms have been developed to solve this system. To establish global convergence, most of these algorithms assumed the operator under consideration to be monotone. In this work, instead of been monotone, our operator under consideration is considered to be pseudomonotone which is more general than the usual monotonicity assumption in most of the existing literature. The proposed method is derivative-free, and also, an inertial step is incorporated to accelerate its speed of convergence. The global convergence of the proposed algorithm is proved under the assumptions that the underlying mapping is Lipschitz continuous and pseudomonotone. Numerical experiments on some test problems are presented to depict the advantages of the proposed algorithm in comparison with some existing ones. Finally, an application of the proposed algorithm is shown in motion control involving a 3-degrees of freedom (DOF) planar robot arm manipulator.

Automated summary

Efforts have been made to develop efficient algorithms for solving system of nonlinear equations. This study presents a derivative-free algorithm that considers the pseudomonotonicity of the operator and incorporates an inertial step to accelerate convergence speed. The global convergence of the proposed algorithm is proven, and numerical experiments demonstrate its advantages over existing algorithms. The application of the algorithm in motion control for a 3-degrees of freedom planar robot arm manipulator is also shown.