Newton's method for class of weakly singular optimal control problems

被引：8

作者：

Ito, K

Kunisch, K

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Karl Franzens Univ Graz, Inst Math, A-8010 Graz, Austria

来源：

SIAM JOURNAL ON OPTIMIZATION | 2000年 / 10卷 / 03期

关键词：

Newton's method; optimal control; singular systems; 2-norm technique;

D O I：

10.1137/S1052623497320840

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Newton's method for optimal control of highly nonlinear partial differential equations is analyzed using a 2-norm technique. We consider the case where neither the linearization of the equality constraint e characterizing the differential equation is surjective nor a second order sufficient optimality condition holds for the topology on which e is well defined. Such problems occur, for instance, in optimal control of semilinear elliptic equations or for parameter estimation problems. Despite the above mentioned difficulties, sufficient conditions for second order convergence are obtained.

引用

页码：896 / 916

页数：21