改进的有限内存BFGS算法的二次终止性质

Quadratic Termination Property of A Modified Limited Memory BFGS Method

二次终止性质是一般拟牛顿法的一个重要性质,但为求解大规模优化问题而设计的有限内存拟牛顿法却不能都保持这种良好性质.为此,针对满足修正拟牛顿方程的有限内存BFGS方法加以研究,证明所提出的方法满足二次终止性质.这对于完善有限内存拟牛顿法的理论体系具有重要作用.

The quadratic termination property is important to general quasi-Newton methods. But the fine property is not shared by all kinds of limited memory quasi-Newton methods for solving large scale optimization. So in order to improve the theory of the limited memory quasi-Newton method, it is significance to study the quadratic termination properties of the limited memory BFGS method, which satisfies the modified quasi-Newton equation, and to prove the quadratic termination property of the proposed method.