Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients

TL;DR

This paper introduces a derivative-free nonlinear least squares framework with dimension reduction and acceleration techniques, specifically applied to estimating parameters in hydraulic dam break models, demonstrating practical effectiveness.

Contribution

It presents a novel derivative-free optimization method with dimension reduction and acceleration, tailored for large-scale nonlinear least squares problems in hydraulic modeling.

Findings

Effective in estimating Manning coefficients in dam models

Shows improved convergence with the proposed acceleration techniques

Numerical results validate the method's practical applicability

Abstract

A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the number of variables is big (for the standards of derivative-free optimization), two dimension-reduction procedures are introduced. One of them is based on iterative subspace minimization and the other one is based on spline interpolation with variable nodes. Each iteration based on those procedures is followed by an acceleration step inspired in the Sequential Secant Method. The practical motivation for this work is the estimation of parameters in Hydraulic models applied to dam breaking problems. Numerical examples of the application of the new method to those problems are given.