Title :
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
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;
Conference_Titel :
Systems, Man and Cybernetics, 2004 IEEE International Conference on
Print_ISBN :
0-7803-8566-7
DOI :
10.1109/ICSMC.2004.1401357
