A New Algorithm with Structured Diagonal Hessian Approximation for Solving Nonlinear Least Squares Problems and Application to Robotic Motion Control

Aliyu Muhammed Awwal, Hassan Mohammad, Mahmoud Muhammad Yahaya, Ahmadu Bappah Muhammadu, Adamu Ishaku

Abstract

Iterative methods for solving nonlinear least-squares problems are of great interest because of their unique structures and wide range of applications. This paper exploits the unique structure and proposes a quasi-Newton diagonal-based approximation for solving this class of problems. Under some appropriate conditions, the search direction satisfies the sufficiently descent condition, and the new method is shown to be globally convergent. The numerical efficiency of the new method is tested on some standard benchmark test problems. Subsequently, the new method is implemented to solve 2 dimensional robotic motion control problem.