A new algorithm for unconstrained optimization problem with the form of sum of squares minimization

In this paper, we present a new algorithm for unconstrained optimization problem with the form of sum of squares minimization that is produced in the procedure of model parameter estimation for nonlinear systems. The new algorithm is composed of conventional BFGS and analytical exact line search where the line search step is calculated by an analytical equation in which the second derivative matrix called Hessian matrix is approximated by the product of Jacobian matrices of objective function. Two case studies show that the new algorithm exhibits excellent convergence performance in terms of computation time and initial values requirement.