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Title of Journal: Optim Lett

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Abbravation: Optimization Letters

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Springer Berlin Heidelberg

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DOI

10.1016/0041-0101(90)90293-g

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1862-4480

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An interior penalty method for a finitedimensiona

Authors: Song Wang Kai Zhang
Publish Date: 2016/06/11
Volume: 12, Issue: 6, Pages: 1161-1178
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Abstract

In this work we study an interior penalty method for a finitedimensional largescale 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 nontrivial test examples are presented to demonstrate the rates of convergence efficiency and usefulness of the method for solving practical problemsKai Zhang wishes to thank the supports from the Philosophy and Social Science Program of Guangdong Province Grant No GD13YYJ01 and the MOE Project of Key Research institute of Humanities and Social Sciences at Universities Grant No 14JJD790041 Project 11001178 partially supported by National Natural Science Foundation of China

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