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

Author

Hu, Yongyou ; Su, Hongye ; Chu, Jian

Author_Institution

Dept. of Chem. & Environ. Eng., Illinois Inst. of Technol., Chicago, IL, USA

Volume

7

fYear

2004

fDate

10-13 Oct. 2004

Firstpage

6108

Abstract

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.

Keywords

Hessian matrices; Jacobian matrices; convergence; minimisation; nonlinear systems; parameter estimation; search problems; Hessian matrix; Jacobian matrices; analytical equation; analytical exact line search; convergence performance; line search step; model parameter estimation; nonlinear systems; objective function; second derivative matrix; sum of squares minimization; unconstrained optimization problem; Algorithm design and analysis; Convergence; Iterative algorithms; Jacobian matrices; Minimization methods; Newton method; Nonlinear systems; Optimization methods; Parameter estimation; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Man and Cybernetics, 2004 IEEE International Conference on

ISSN

1062-922X

Print_ISBN

0-7803-8566-7

Type

conf

DOI

10.1109/ICSMC.2004.1401357

Filename

1401357