For Solving Nonlinear Constrained Optimization Problems Modified Bfgs Method

This paper is based on the modified BFGS formula proposed by Aiping Liao[6]. It discusses about the choice of the parameter(δk,γk) and proposes a series of parameter choices. The first part of this paper mainly introduces the history of BFGS algorithm and the present situation of modified BFGS algorithm.The second part of this paper firstly proposes a class of parameter (δk,γk) by imitating Liao's method, so that a new BFGS formula is obtained. The global convergence,local superlinear convergence and numerical experiment are given in succession. Then, in order to obtain the global convergence and local superlinear convergence of the general modified BFGS algorithm, a general attribute of parameter (δk,γk) is given. In the part of numerical experiment, a specific parameter is given to parameter (δk,γk). At last, new quasi-Newton equations are introduced into the modified BFGS formula, so a new modified BFGS algorithm with the general condition of parameter (δk,γk) which is global convergent and local superlinear convergent is obtained. As a corollary of this algorithm, another general condition of parameter (δk,γk) is obtained.