A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs

被引：28

作者：

Hintermueller, M. ^{[1
,2
]}

Kopacka, I. ^{[2
]}

机构：

[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

[2] Karl Franzens Univ Graz, Dept Math & Sci Comp, A-8010 Graz, Austria

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2011年 / 50卷 / 01期

基金：

奥地利科学基金会;

关键词：

Constrained optimal control; Elliptic variational inequality; MPEC; Mathematical programs with complementarity constraints; C-stationarity; Nonlinear multigrid; MATHEMATICAL PROGRAMS; COMPLEMENTARITY CONSTRAINTS; VARIATIONAL-INEQUALITIES; OPTIMALITY CONDITIONS; STATIONARITY; SCHEME;

D O I：

10.1007/s10589-009-9307-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

An optimal control problem governed by an elliptic variational inequality of the first kind and bilateral control constraints is studied. A smooth penalization technique for the variational inequality is applied and convergence of stationary points of the subproblems to an E-almost C-stationary point of the limit problem is shown. The subproblems are solved using a full approximation multigrid scheme (FAS) and alternatively a multigrid method of the second kind for which a convergence result is given. An overall algorithmic concept is provided and its performance is discussed by means of examples.

引用

页码：111 / 145

页数：35

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