New structured spectral gradient methods for nonlinear least squares with application in robotic motion control problems

Abstract

The recently introduced structured spectral Barzilai–Borwein-like (BB-like) gradient algorithms in (Optimization Methods and Software, 4(37), pp:1269–1288, 2022) which utilize substantial information of the Hessian matrix are efficient for solving nonlinear least squares (NLS) problems. However, a safeguarding technique is required for the spectral parameters in their formulation to be well-defined. In this paper, we present another spectral gradient algorithm that improves the efficiency of those formulations where the proposed structured spectral parameter does not necessarily require a safeguarding strategy. Moreover, with the aid of nonmonotone line search and some standard assumptions, we show the global convergence of the algorithm. In addition, the numerical results of the proposed algorithm on some benchmark problems are encouraging. Furthermore, we apply the algorithm to solving a motion control problem.