Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Ge Ren-Dong and Xia Zun-Quan
Pages: [17] - [35]
Received Date: July 20, 2009
Submitted by:
A modified BFGS algorithm to solve the unconstrained optimization of a
convex function is presented in this paper, whose Hessian matrix of
the minimum point is of rank defects. The idea of the algorithm is to
give a modified part of the convex function to obtain an equivalent
model, then simplify the model to obtain the modified BFGS algorithm.
The global convergence property of the algorithm is proved in this
paper. And compared with the Tensor algorithm, it is shown that this
method is more efficient for solving unconstrained optimization, whose
object function is of rank defects as the latter’s restriction
nonconvex function, unconstrained programme, BFGS algorithm, locally superlinear convergence, Quasi-Newton method.
