An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering
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 contain...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
Springer Verlag
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/69495 |
| _version_ | 1848762056867577856 |
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| author | Wang, Song Zhang, K. |
| author_facet | Wang, Song Zhang, K. |
| author_sort | Wang, Song |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T10:41:30Z |
| format | Journal Article |
| id | curtin-20.500.11937-69495 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:41:30Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-694952019-06-17T01:15:13Z An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering Wang, Song Zhang, K. 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. 2018 Journal Article http://hdl.handle.net/20.500.11937/69495 10.1007/s11590-016-1050-4 Springer Verlag fulltext |
| spellingShingle | Wang, Song Zhang, K. An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title | An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title_full | An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title_fullStr | An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title_full_unstemmed | An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title_short | An interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| title_sort | interior penalty method for a finite-dimensional linear complementarity problem in financial engineering |
| url | http://hdl.handle.net/20.500.11937/69495 |