An Improved BFGS Algorithm Based On New Quasi-Newton Equation And Its Convergence Analysis

With the minimum pay to obtain the biggest benefit is the goal that we want to achieve when do anything or make decisions about something,however,the study of mathematical theory usually establish a mathematical model under reasonable assumptions and then transform the problem to the solution of an unconstrained optimization problem.After several decades of theoretical development,the effective way to solve this kind of problem is BFGS algorithm in quasi-Newton methods.Based on the study of many scholars,this paper make some progress on standard BFGS algorithm and results have been obtained.Here are some specific research contents in details:First,by introducing the parameter ? ?[0,1] and with the known updating formulakB proposed by Biggs and Yuan,this paper proposed an improved updating formula(kB),when the parameters are taken at two ends,the equation can be regarded as the formula proposed by two scholars,and make sure the rationality of the presented formula through a further necessary explanation on this updating formula based on literature review and research ideas,and then proposed an improved BFGS algorithm(MBFGS)in the basis of improved updating formula than mentioned in the above.Second,proposed an improved BFGS algorithm(RMBFGS)that combined with the new quasi-Newton equation and an improved updating formula that is proposed in above,and given the algorithm convergence proof including global convergence and local superliner convergence.At the same time,numerical experiments show that the proposed algorithm is superior to the standard BFGS algorithm and other equivalent BFGS algorithm.At last,a kind of L-RMBFGS algorithm is derived which can be applied to solve large scale of unconstrained optimization problem referring the line of thinking inL-BFGS algorithm.