Regularization for semilinear elliptic optimal control problems with pointwise state and control constraints

被引：0
作者：
Klaus Krumbiegel
Ira Neitzel
Arnd Rösch
机构：
[1] Weierstrass Institute for Applied Mathematics and Stochastics,Fakultät II–Mathematik und Naturwissenschaften
[2] Nonlinear Optimization and Inverse Problems,Department of Mathematics
[3] Technische Universität Berlin,undefined
[4] Universität Duisburg-Essen,undefined
来源：
Computational Optimization and Applications | 2012年 / 52卷
关键词：
Optimal control; Semilinear elliptic equation; State constraints; Regularization; Virtual control; Second order sufficient conditions;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. We show that sufficient second order optimality conditions for regularized problems with small regularization parameter can be obtained from a second order sufficient condition assumed for the unregularized problem. Moreover, error estimates with respect to the regularization parameter are derived.
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页码：181 / 207
页数：26
相关论文
共 55 条
[1]  
Arada N.(2000)Optimal control problems with mixed control-state constraints SIAM J. Control Optim. 39 1391-1407
[2]  
Raymond J.P.(1999)Primal-dual strategy for constrained optimal control problems SIAM J. Control Optim. 37 1176-1194
[3]  
Bergounioux M.(1986)Control of an elliptic problem with pointwise state constraints SIAM J. Control Optim. 4 1309-1322
[4]  
Ito K.(1993)Boundary control of semilinear elliptic equations with pointwise state constraints SIAM J. Control Optim. 31 993-1006
[5]  
Kunisch K.(2008)Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints SIAM J. Optim. 19 616-643
[6]  
Casas E.(2002)Error estimates for the finite-element approximation of a semilinear elliptic control problem Control Cybern. 31 695-712
[7]  
Casas E.(2010)Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems ESAIM: COCV 16 581-600
[8]  
Casas E.(2008)Error estimates for the Lavrentiev regularization of elliptic optimal control problems Inverse Probl. 24 195-212
[9]  
de los Reyes J.C.(2008)Error estimates for the regularization of optimal control problems with pointwise control and state constraints ZAA 27 776-792
[10]  
Tröltzsch F.(2008)Convergence analysis of the SQP method for nonlinear mixed-constrained elliptic optimal control problems ZAMM 88 679-687
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