A structured quasi-Newton algorithm with nonmonotone search strategy for structured NLS problems and its application in robotic motion control

This article proposes a structured diagonal Hessian approximation for solving non-linear least-squares (NLS) problems. We devised a modified structured matrix that satisfies the weak secant equation. This structured matrix is then used to derive the structured diagonal approximation of the Hessian in a similar pattern as the paper of Andrei (2019). By solving a minimization problem, we derived the formulation of the structured diagonal approximation of the Hessian by minimizing the deviation between any two successive updates and the trace of the updated diagonal matrix so that the modified structured weak secant equation is satisfied. More so, we show the global convergence of the proposed algorithm under some standard assumptions. Comparative numerical experiments on some benchmark problems with 308 instances show the efficacy of the proposed algorithm. Finally, we reveal the applicability of the proposed algorithm in the motion control of two planar robots.