TITLE:
Solving Large Scale Unconstrained Minimization Problems by a New ODE Numerical Integration Method
AUTHORS:
Tianmin Han, Xinlong Luo, Yuhuan Han
KEYWORDS:
Unconstrained Minimization Problem, Gradient Equations, Quadratic Model, Spectral Radius, ODE Numerical Integration
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.5,
May
6,
2011
ABSTRACT: In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of ; or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.