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Augmented Lagrangian Active Set Methods for Obstacle Problems

Author

Listed:
  • T. Kärkkäinen

    (University of Jyväskylä)

  • K. Kunisch

    (University of Graz)

  • P. Tarvainen

Abstract

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.

Suggested Citation

  • T. Kärkkäinen & K. Kunisch & P. Tarvainen, 2003. "Augmented Lagrangian Active Set Methods for Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 499-533, December.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006687.57272.b6
    DOI: 10.1023/B:JOTA.0000006687.57272.b6
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    Cited by:

    1. Arregui, Iñigo & Salvador, Beatriz & Vázquez, Carlos, 2017. "PDE models and numerical methods for total value adjustment in European and American options with counterparty risk," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 31-53.
    2. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Corrigendum to ``Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model''," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    3. Salvador, Beatriz & Oosterlee, Cornelis W., 2021. "Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    4. Calvo-Garrido, Maria del Carmen & Pascucci, Andrea & Vázquez Cendón, Carlos, 2012. "Mathematical analysis and numerical methods for pricing pension plans allowing early retirement," MPRA Paper 36494, University Library of Munich, Germany.
    5. Calvo-Garrido, María del Carmen & Vázquez, Carlos, 2015. "Effects of jump-diffusion models for the house price dynamics in the pricing of fixed-rate mortgages, insurance and coinsurance," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 730-742.

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