成组BFGS修正的紧凑形式与成组记忆修正算法  

REPRESENTATION OF MULTIPLE BFGS'S UPDATINGMATRIX AND MULTIPLE VERSION OF BFGS'S METHODWITH LIMITED STORAGE

作　　者：顾桂定[1] 王德人[2] 

机构地区：[1]复旦大学数学所 [2]上海大学数学系

出　　处：《计算数学》1999年第4期417-428,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金!19971057;上海市高校科技发展基金

摘　　要：In 1994, O’leary and Yeremin extended the quasi-Newton method for minimizing a collection of functions with a common Hessian matrix to the block version,and discussed some algebraic properties of this block quasi-Newton method. In thispaper, we derive compact representations of the block BFGS’s updating matrices.These representations allow us to efficiently implement limited memory methods,e.g., the limited memory BFGS method, for minimizing a collection of functionswith a common Hessian matrix. The method relieves the requirement for the storage counts and has the savings in the operation counts, in particular, for large scaleproblems. The numerical experiments for the multiple unconstrained optimizationproblems show that the method works efficiently. Compared with O’Leary’s multiple version of BFGS method, our multiple version of the limited memory BFGSmethod is more efficient in the total operation counts and the storage counts.In 1994, O'leary and Yeremin extended the quasi-Newton method for minimizing a collection of functions with a common Hessian matrix to the block version,and discussed some algebraic properties of this block quasi-Newton method. In thispaper, we derive compact representations of the block BFGS's updating matrices.These representations allow us to efficiently implement limited memory methods,e.g., the limited memory BFGS method, for minimizing a collection of functionswith a common Hessian matrix. The method relieves the requirement for the storage counts and has the savings in the operation counts, in particular, for large scaleproblems. The numerical experiments for the multiple unconstrained optimizationproblems show that the method works efficiently. Compared with O'Leary's multiple version of BFGS method, our multiple version of the limited memory BFGSmethod is more efficient in the total operation counts and the storage counts.

关 键 词：BFGS算法 成组型算法 有记忆算法 拟牛顿法 

分 类 号：O242.23[理学—计算数学]