A TYPE OF MODIFIED BFGS ALGORITHM WITH RANK DEFECTS AND ITS GLOBAL CONVERGENCE IN CONVEX MINIMIZATION

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