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    An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering

    267712.pdf (2.955Mb)
    Access Status
    Open access
    Authors
    Wang, Song
    Zhang, K.
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Wang, S. and Zhang, K. 2018. An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering. Optimization Letters. 12 (6): pp. 1161-1178.
    Source Title
    Optimization Letters
    DOI
    10.1007/s11590-016-1050-4
    ISSN
    1862-4472
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    Remarks

    The final publication is available at Springer via 10.1007/s11590-016-1050-4

    URI
    http://hdl.handle.net/20.500.11937/69495
    Collection
    • Curtin Research Publications
    Abstract

    In this work we study an interior penalty method for a finite-dimensional large-scale linear complementarity problem (LCP) arising often from the discretization of stochastic optimal problems in financial engineering. In this approach, we approximate the LCP by a nonlinear algebraic equation containing a penalty term linked to the logarithmic barrier function for constrained optimization problems. We show that the penalty equation has a solution and establish a convergence theory for the approximate solutions. A smooth Newton method is proposed for solving the penalty equation and properties of the Jacobian matrix in the Newton method have been investigated. Numerical experimental results using three non-trivial test examples are presented to demonstrate the rates of convergence, efficiency and usefulness of the method for solving practical problems.

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