Journal of Optimization Theory and Applications

, Volume 119, Issue 3, pp 499–533 | Cite as

Augmented Lagrangian Active Set Methods for Obstacle Problems

  • T. Kärkkäinen
  • K. Kunisch
  • P. Tarvainen


Active set strategies for two-dimensional and three-dimensional, unilateral and bilateral obstacle problems are described. Emphasis is given to algorithms resulting from the augmented Lagrangian (i.e., primal-dual formulation of the discretized obstacle problems), for which convergence and rate of convergence are considered. For the bilateral case, modifications of the basic primal-dual algorithm are also introduced and analyzed. Finally, efficient computer realizations that are based on multigrid and multilevel methods are suggested and different aspects of the proposed techniques are investigated through numerical experiments.

Obstacle problems active set strategies augmented Lagrangian methods multigrid and multilevel methods 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • T. Kärkkäinen
    • 1
  • K. Kunisch
    • 2
  • P. Tarvainen
    • 3
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland
  2. 2.Institute for MathematicsUniversity of GrazGrazAustria
  3. 3.JyväskyläFinland

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