基于新拟牛顿方程的一类改进BFGS算法  

A Class of Modified BFGS Algorithm Based on the New Quasi-Newton Equation

作　　者：王海滨[1] 

机构地区：[1]南通职业大学基础部,江苏南通226007

出　　处：《淮海工学院学报（自然科学版）》2004年第1期7-10,共4页Journal of Huaihai Institute of Technology:Natural Sciences Edition

摘　　要：针对无约束最优化问题 ,在已建立的一类新拟牛顿方程 Bk+ 1sk=yk =yk+ γks Tksksk的基础上 ,证明了满足新拟牛顿方程的一类改进 BFGS算法在修正矩阵 Bk 中参数 tk 满足 | 1 - tk|≤t′‖ sk‖ ( t′为任一常数 ) ,且目标函数一致凸的条件下 ,具有全局收敛性 .基于新方程的改进 BFGS算法产生的修正矩阵比传统拟牛顿方程产生的修正矩阵更接近于A class of modified BFGS algorithm based on the new quasi-Newton equation Bk+1sk=k=yk+γksTksksk is presented in this paper to solve the unconstrained optimization problem, and the global convergence is proved under the condition that the objective function is uniformly convex, the parameter k satisfies |1-k|≤t′‖sk‖ (t′ is a constant). The update matrix generated by modified BFGS algorithm based on the new quasi-Newton equation is more approximate to Hessian matrix than the one based on the traditional quasi-Newton equation.

关 键 词：新拟牛顿方程 改进BFGS算法 全局收敛性 修正矩阵 无约束最优化 

分 类 号：O224[理学—运筹学与控制论]