NONSMOOTH NEWTON METHODS FOR SET-VALUED SADDLE POINT PROBLEMS

被引：11

作者：

Graeser, Carsten ^{[1
]}

Kornhuber, Ralf ^{[1
]}

机构：

[1] Free Univ Berlin, Inst Math 2, D-14195 Berlin, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 02期

关键词：

set-valued saddle point problems; nonsmooth Newton methods; Uzawa algorithms; active set preconditioners; FINITE-ELEMENT APPROXIMATION; MULTIGRID METHODS; CONVERGENCE RATE; ALGORITHMS; SMOOTHERS; EQUATIONS;

D O I：

10.1137/060671012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new class of iterative schemes for large scale set-valued saddle point problems as arising, e.g., from optimization problems in the presence of linear and inequality constraints. Our algorithms can be regarded either as nonsmooth Newton-type methods for the nonlinear Schur complement or as Uzawa-type iterations with active set preconditioners. Numerical experiments with a control constrained optimal control problem and a discretized Cahn-Hilliard equation with obstacle potential illustrate the reliability and efficiency of the new approach.

引用

页码：1251 / 1273

页数：23

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