A Class Of Modified Quasi-newton Algorithm

Optimization design is widely used in real life.We can solve the problems in real life through the basic knowledge and calculation methods in numerical optimization.We can use scientific calculation methods and network programming to make our work more efficient and scientific.Therefore,it is of great significance to study the computational methods of unconstrained optimization problems.Quasi-Newton method is one of the most effective methods in solving nonlinear equations and optimization calculations.Nowadays,optimization software contains a large number of quasi-Newton algorithms to solve unconstrained,constrained and large-scale optimization problems.It is particularly important to further study the properties and applications of quasi-Newton algorithm.This paper mainly studies a class of modified quasi-Newton algorithm for unconstrained optimization problems.The BFGS method is widely used in numerous optimization software and is a fundamental and critical quasi-Newton method for solving unconstrained optimization problems.One of the amusing properties of the BFGS method is its selfcorrecting character.To acquire greater performance of BFGS method under this property,a new single parameter scaling the BFGS method for nonconvex functions is presented in this paper.A modified weak Wolfe-Powell line search,namely,YuanWei-Lu(YWL)line search is also introduced,and the global convergence of the BFGS method mentioned under YWL line search is proved.Preliminary numerical experiments show that the computational efficiency of this method is competitive.Secondly,a new two-parameter scaling BFGS method is proposed by scaling the first two terms and the last term of the standard BFGS method with different parameters.Furthermore,based on the weak Wolfe-Powell line search,the global convergence of the new two-parameter scaled BFGS method is established for nonconvex functions.Experiments show that the new method is more effective than the standard BFGS method.