A PRIORI ERROR ESTIMATES FOR A STATE-CONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEM

被引：13
|
作者：
Roesch, Arnd [1 ]
Steinig, Simeon [2 ]
机构：
[1] Univ Duisburg Essen, Fak Math, D-47057 Duisburg, Germany
[2] Univ Stuttgart, Inst Angew Anal & Numer Simulat, D-70569 Stuttgart, Germany
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2012年 / 46卷 / 05期
关键词：
Elliptic optimal control problem; state constraint; a priori error estimates; REGULAR LAGRANGE MULTIPLIERS; FINITE-ELEMENT APPROXIMATION; ACTIVE SET STRATEGY; POINTWISE CONTROL; CONVERGENCE; EQUATIONS; BOUNDARY;
D O I：
10.1051/m2an/2011076
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We examine an elliptic optimal control problem with control and state constraints in R-3. An improved error estimate of O(h(s)) with 3/4 <= s <= 1-epsilon is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.
引用
收藏
页码：1107 / 1120
页数：14
相关论文
共 50 条
  • [1] A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems
    Francesco Ludovici
    Ira Neitzel
    Winnifried Wollner
    Journal of Optimization Theory and Applications, 2018, 178 : 317 - 348
  • [2] A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems
    Ludovici, Francesco
    Neitzel, Ira
    Wollner, Winnifried
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 178 (02) : 317 - 348
  • [3] A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems
    Zhang, Juan
    Song, Jiabin
    Chen, Huanzhen
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2023, 15 (03) : 568 - 582
  • [4] Error estimates for integral constraint regularization of state-constrained elliptic control problems
    B. Jadamba
    A. Khan
    M. Sama
    Computational Optimization and Applications, 2017, 67 : 39 - 71
  • [5] Error estimates for integral constraint regularization of state-constrained elliptic control problems
    Jadamba, B.
    Khan, A.
    Sama, M.
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2017, 67 (01) : 39 - 71
  • [6] A priori error estimates for elliptic optimal control problems with a bilinear state equation
    Kroener, Axel
    Vexler, Boris
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (02) : 781 - 802
  • [7] Convexifying State-Constrained Optimal Control Problem
    Lee, Donggun
    Deka, Shankar A.
    Tomlin, Claire J.
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2023, 68 (09) : 5608 - 5615
  • [8] State-constrained optimal control of nonlinear elliptic variational inequalities
    Serovajsky, S.
    OPTIMIZATION LETTERS, 2014, 8 (07) : 2041 - 2051
  • [9] State-constrained optimal control of nonlinear elliptic variational inequalities
    S. Serovajsky
    Optimization Letters, 2014, 8 : 2041 - 2051
  • [10] Reliable a posteriori error estimation for state-constrained optimal control
    Roesch, A.
    Siebert, K. G.
    Steinig, S.
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2017, 68 (01) : 121 - 162
12345