The q-Gauss-Newton method for unconstrained nonlinear optimization

TL;DR

The paper introduces a q-Gauss-Newton method for unconstrained nonlinear optimization that accelerates convergence by approximating second-order derivatives with first-order q-Jacobian matrices, demonstrating improved speed and effectiveness.

Contribution

It presents a novel q-Gauss-Newton algorithm that leverages q-second order derivatives approximation, offering faster convergence compared to traditional methods.

Findings

The q-GN method converges when initial guess is close to the solution.

The algorithm finds optimal solutions effectively.

It speeds up the iterative optimization process.

Abstract

A q-Gauss-Newton algorithm is an iterative procedure that solves nonlinear unconstrained optimization problems based on minimization of the sum squared errors of the objective function residuals. Main advantage of the algorithm is that it approximates matrix of q-second order derivatives with the first-order q-Jacobian matrix. For that reason, the algorithm is much faster than q-steepest descent algorithms. The convergence of q-GN method is assured only when the initial guess is close enough to the solution. In this paper the influence of the parameter q to the non-linear problem solving is presented through three examples. The results show that the q-GD algorithm finds an optimal solution and speeds up the iterative procedure.