MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS IN FUNCTION SPACE: C- AND STRONG STATIONARITY AND A PATH-FOLLOWING ALGORITHM

被引：65
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 & Comp Sci, A-8010 Graz, Austria
来源：
SIAM JOURNAL ON OPTIMIZATION | 2009年 / 20卷 / 02期
基金：
奥地利科学基金会;
关键词：
constrained optimal control; mathematical programs with complementarity constraints; MPEC; MPCC; Moreau-Yosida regularization; semismooth Newton method; C- and strong stationarity; OPTIMALITY CONDITIONS; VARIATIONAL-INEQUALITIES; MINIMIZATION; CONVERGENCE;
D O I：
10.1137/080720681
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An optimal control problem governed by an elliptic variational inequality is studied. The feasible set of the problem is relaxed, and a path-following-type method is used to regularize the constraint on the state variable. First order optimality conditions for the relaxed-regularized subproblems are derived, and convergence of stationary points with respect to the relaxation and regularization parameters is shown. In particular, C- and strong stationarity as well as variants thereof are studied. The subproblems are solved by using semismooth Newton methods. The overall algorithmic concept is provided, and its performance is discussed by means of examples, including problems with bilateral constraints and a nonsymmetric operator.
引用
收藏
页码：868 / 902
页数：35
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