Skip to main content
SpringerLink
Log in

State-constrained optimal control of an elliptic equation with its right-hand side used as control function

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

A grid approximation is considered for the control-and-state-constrained optimal control of a linear elliptic equation with its right-hand side used as a control function. The resulting finite-dimensional problem is solved by using iterative methods, whose convergence is analyzed theoretically and numerically. Numerical results produced by different methods are compared.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Gill, W. Murray, and M. Wright, Practical Optimization (Academic, London, 1981).

    MATH  Google Scholar 

  2. D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods (Academic, New York, 1982).

    MATH  Google Scholar 

  3. Large-Scale PDE-Constrained Optimization, Ed. by L. T. Biegler, O. Ghattas, M. Heinkenschloss, and B. van BloemenWaanders (Springer-Verlag, Berlin, 2003).

    MATH  Google Scholar 

  4. M. Bergounioux, Augmented Lagrangian Method for Distributed Optimal Control Problems with State Constraints, Optim. Theory Appl. 78, 493 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Bergounioux, V. Haddou, M. Hintermuller, and K. Kunisch, A Comparison of a Moreau-Yosida-Based Active Set Strategy and Interior Point Methods for Constrained Optimal Control Problems, SIAM J. Optim. 11, 495 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Bergounioux and K. Kunisch, Primal-Dual Strategy for State-Constrained Optimal Control Problems, Comput. Optim. Appl. 22, 193 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. I. Ekeland and R. Temam, Convex Analysis and Variational Problems (North-Holland, Amsterdam, 1976; Mir, Moscow, 1979).

    MATH  Google Scholar 

  8. A. V. Lapin, Iterative Methods for Solving Grid Variational Inequalities (Kazan. Gos. Univ., Kazan, 2008) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Statistics, Kazan (Volga Region) Federal University, ul. Kremlevskaya 18, Kazan, 420008, Russia

    A. V. Lapin

  2. Chebotarev Research Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, Universitetskaya ul. 17, Kazan, 420008, Tatarstan, Russia

    M. G. Khasanov

Authors
  1. A. V. Lapin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. G. Khasanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Lapin.

Additional information

Original Russian Text © A.V. Lapin, M.G. Khasanov, 2010, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2010, Vol. 152, No. 4, pp. 56–67.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lapin, A.V., Khasanov, M.G. State-constrained optimal control of an elliptic equation with its right-hand side used as control function. Lobachevskii J Math 32, 453–462 (2011). https://doi.org/10.1134/S1995080211040287

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080211040287

Keywords and phrases

Search

Navigation