On diagonally structured scheme for nonlinear least squares and data-fitting problems

Abstract

Recently, structured nonlinear least-squares (NLS) based algorithms gained considerable emphasis from researchers; this attention may result from increasingly applicable areas of these algorithms in different science and engineering domains. In this article, we coined a new efficient structured-based NLS algorithm. We developed a diagonal Hessian-based formulation for solving NLS problems. We derived the quasi-Newton update based on a diagonal matrix scheme subject to a modified structured secant condition. Also, we show that the algorithm search direction satisfies a sufficient descent condition under some standard assumptions. Subsequently, we also prove the global convergence of the algorithm and then eventually show the linear convergence rate for strongly convex functions. Furthermore, we numerically experimented with the proposed algorithm on benchmark test functions available in the literature. Finally, in the scheme, we apply the method to solve some data-fitting problems.