| Optimization problems are often encountered in practical applications.They are usually solved by using the basic knowledge and calculation methods in numerical optimization,establishing the corresponding mathematical models of the problems under reasonable assumptions,and transforming them into unconstrained optimization problems to solve,which is one of the most convenient methods to solve such problems.After decades of theoretical development,quasi-Newton method stands out among many methods for solving optimization problems,and is one of the most effective solutions at present.Now,the quasi-Newton method is included in most optimization software to solve unconstrained problems,constrained problems and large-scale optimization problems.Therefore,it is particularly important to further study the theoretical knowledge and applications of quasi-Newton method.This paper mainly studies BFGS algorithm in quasi-Newton method.Through reading a large number of documents and summarizing the existing algorithm improvement strategies,this paper improves the BFGS algorithm from the perspective of the information retention of the objective function,the global convergence of the method and the effectiveness of the algorithm.Here are some specific research contents in details:Firstly,by studying the relevant theoretical knowledge of quasi-Newton method,we know one of the most important characteristics of BFGS algorithm is the self-correction property.In order to make BFGS algorithm have better performance under this property,this paper constructs a new quasi-Newton equation based on the introduction of damping technology,in which parameter?is introduced,which is updated by the gradient value and the function value information,thereby improves the correction formula _kB and proposes GBFGS algorithm.This paper proves the global convergence of the GBFGS algorithm based on the weak Wolfe-Powell line search condition.Experiments show that the proposed GBFGS algorithm is more effective than the standard BFGS algorithm.Secondly,considering that with the development of the times,it is mostly to solve high-dimensional problems at this stage.Therefore,a limited memory framework is introduced to reduce the storage space required by the algorithm.Based on this,the L-GBFGS algorithm suitable for solving large-scale unconstrained optimization problems is proposed,and the formula is deduced.Finally,the L-GBFGS algorithm,which introduces a limited memory framework,is applied to the neural network algorithm by replacing the gradient class algorithm in the original neural network algorithm,and optimising the parameters in the network.It can be used to solve the problem of non-invasive blood glucose concentration prediction.By analysing the calculation results of the problem,it shows that the quasi-Newton neural network model is effective and feasible in solving the problem of non-invasive blood glucose concentration prediction. |
