Studying the convergence property of finite stored BFGS algorithm,under condi- tion of step size in search with lower bound,the global convergence of algorithm for general convex function is proved.

Based on this linear independence theory, a modified limited memory BFGS method is deve loped.

The paper analyses the problem on circular creep of thick - wall cylinder, and the recurrence formular of the nonlinear finite element method based on the BFGS method is given, Further more, adopting the ADINA program, the equivalent stress of the thick - wall cylinder is calculated out, which proves a better convergence and numerical stability of BFGS method than that of N - R method.

Application of BP network based on BFGS algorithm in BTP prediction;

BFGS algorithm is one of the most effective methods in solving the non-constrained optimization problems.

The advantages and disadvantages of BFGS algorithm and simulated annealing algorithm were studied and considering BFGS s good local searching ability and simulated annealing algorithm global searching ability,a mixed BFGS-SA algorithm was proposed in the paper.

This paper,based on BFGS method,presents an artificial neural network model for unconstrained optimization problems,and some stability properties of the neural network are discussed.

In this paper,we present a modified BFGS method,which satisfies the quasi-Newton funtion proposed by Wei~(11).

In this thesis, we first propose a modified limited memory BFGS method for solving non-convex minimization problem, then we give a compact limited memory BFGS method for convex optimization.