A penalty approach to a discretized double obstacle problem with derivative constraints
This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating th...
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| Format: | Journal Article |
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Springer
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/43515 |
| _version_ | 1848756717632880640 |
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| author | Wang, Song |
| author_facet | Wang, Song |
| author_sort | Wang, Song |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating the mixed nonlinear complementarity problem representing the Karush-Kuhn-Tucker conditions of the optimization problem. We then show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the equation. Numerical experiments, carried out on a non-trivial test problem to verify the theoretical finding, show that the computed rates of convergence match the theoretical ones well. |
| first_indexed | 2025-11-14T09:16:38Z |
| format | Journal Article |
| id | curtin-20.500.11937-43515 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:16:38Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-435152019-02-19T05:35:05Z A penalty approach to a discretized double obstacle problem with derivative constraints Wang, Song Mixed nonlinear complementarity problem Convergence rates Variational inequalities Global optimizer Penalty method Double obstacle problem Bounded linear constraints This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating the mixed nonlinear complementarity problem representing the Karush-Kuhn-Tucker conditions of the optimization problem. We then show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the equation. Numerical experiments, carried out on a non-trivial test problem to verify the theoretical finding, show that the computed rates of convergence match the theoretical ones well. 2015 Journal Article http://hdl.handle.net/20.500.11937/43515 10.1007/s10898-014-0262-3 Springer fulltext |
| spellingShingle | Mixed nonlinear complementarity problem Convergence rates Variational inequalities Global optimizer Penalty method Double obstacle problem Bounded linear constraints Wang, Song A penalty approach to a discretized double obstacle problem with derivative constraints |
| title | A penalty approach to a discretized double obstacle problem with derivative constraints |
| title_full | A penalty approach to a discretized double obstacle problem with derivative constraints |
| title_fullStr | A penalty approach to a discretized double obstacle problem with derivative constraints |
| title_full_unstemmed | A penalty approach to a discretized double obstacle problem with derivative constraints |
| title_short | A penalty approach to a discretized double obstacle problem with derivative constraints |
| title_sort | penalty approach to a discretized double obstacle problem with derivative constraints |
| topic | Mixed nonlinear complementarity problem Convergence rates Variational inequalities Global optimizer Penalty method Double obstacle problem Bounded linear constraints |
| url | http://hdl.handle.net/20.500.11937/43515 |