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    A penalty approximation method for a semilinear parabolic double obstacle problem

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    Fulltext not available
    Authors
    Zhou, Y.
    Wang, Song
    Yang, X.
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhou, Y. and Wang, S. and Yang, X. 2014. A penalty approximation method for a semilinear parabolic double obstacle problem. Journal of Global Optimization. 60: pp. 531-550.
    Source Title
    Journal of Global Optimization
    DOI
    10.1007/s10898-013-0122-6
    ISSN
    0925-5001
    URI
    http://hdl.handle.net/20.500.11937/15410
    Collection
    • Curtin Research Publications
    Abstract

    In this work, we present a novel power penalty method for the approximation of a global solution to a double obstacle complementarity problem involving a semilinear parabolic differential operator and a bounded feasible solution set.We first rewrite the double obstacle complementarity problem as a double obstacle variational inequality problem. Then, we construct a semilinear parabolic partial differential equation (penalized equation) for approximating the variational inequality problem.We prove that the solution to the penalized equation converges to that of the variational inequality problem and obtain a convergence rate that is corresponding to the power used in the formulation of the penalized equation. Numerical results are presented to demonstrate the theoretical findings.

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