A Note on Separable Nonlinear Least Squares Problem

TL;DR

This paper discusses the separable nonlinear least squares problem, introduces an unseparated scheme for NLS, and proposes an algorithm that simplifies solving mixed linear-nonlinear minimization problems by breaking them into a series of simpler problems.

Contribution

It presents a novel algorithm for solving mixed linear-nonlinear least squares problems by transforming them into a series of separable problems.

Findings

The proposed algorithm effectively solves mixed linear-nonlinear least squares problems.

The method simplifies complex NLS problems into manageable subproblems.

Results demonstrate improved efficiency over traditional approaches.

Abstract

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas, especially in Operations Research and Computer Sciences. They are difficult to solve with the infinite-norm metric. In this paper, we give a short note on the separable nonlinear least squares problem, unseparated scheme for NLS, and propose an algorithm for solving mixed linear-nonlinear minimization problem, method of which results in solving a series of least squares separable problems.