NEWTON METHOD WITH A MODEL TRUST REGION MODIFICATION
NEWTON METHOD WITH A MODEL TRUST REGION MODIFICATION
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DOI：
10.1137/0719026
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发表时间：
1982-01-01
影响因子：
2.9
通讯作者：
SORENSEN, DC
中科院分区：
文献类型：
--
作者：
SORENSEN, DC
提出并分析了一种求解无约束极小化问题的修正牛顿法。修正是基于模型信赖域方法。这份报告包含了一个彻底的分析，局部约束二次最小化，出现在修改后的牛顿迭代的子问题。几个有前途的替代方案，解决这些子问题的方式，克服一定的理论困难，暴露了这种分析。非常强的收敛性的结果，提出有关的最小化算法。特别是，显式使用二阶信息是合理的，证明迭代收敛到一个点，满足二阶必要条件最小化。除了非常病态的情况下，这种情况发生时，该算法是适用于连续的二阶偏导数的问题。
A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization. With the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives.