화학공학소재연구정보센터
SIAM Journal on Control and Optimization, Vol.49, No.2, 339-362, 2011
METRIC REGULARITY OF NEWTON'S ITERATION
For a version of Newton's method applied to a generalized equation with a parameter, we extend the paradigm of the Lyusternik-Graves theorem to the framework of a mapping acting from the pair "parameter-starting point" to the set of corresponding convergent Newton sequences. Under ample parameterization, metric regularity of the mapping associated with convergent Newton sequences becomes equivalent to the metric regularity of the mapping associated with the generalized equation. We also discuss an inexact Newton method and present an application to discretized optimal control.