摘要
本文提出一类折线搜索的信赖域方法,用于解无约束最优化问题.这些方法通过对一般对称矩阵的Bunch-Parlett分解来产生搜索路径.我们证明在一些较弱的条件下,算法是整体收敛的;对一致凸函数,是二次收敛的;并且在由算法得到的点列的任意聚点上,连续可微的目标函数的Hesse阵都是正定或半正定的.一些数值结果表明这种新的方法是非常有效的.
In this paper, we propose a class of trust region dogleg methods for nonlinear optimization problems. We find an approximate solution δ* of the quadratic subproblem by piecewise linear paths, which are called dogleg paths and obtained by employing Bunch-Parlett factorization for general symmetric matrices.We prove that these methods are global convergent for continuous differentiable functions and second-order convergent for uniformly convex objective functions. Also the Hessian matrices of the objective function, if they exist, are positive definite or positive semidefinite at all accumulation points of {xk} obtained by the methods.
出处
《应用数学与计算数学学报》
2002年第1期47-56,共10页
Communication on Applied Mathematics and Computation
基金
教育部基金项目资助.
