An exact penalty function method for nonlinear mixed discrete programming problems
In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additi...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer Verlag
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/39347 |
| _version_ | 1848755567328231424 |
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| author | Changjun, Y. Teo, Kok Lay Bai, Y. |
| author_facet | Changjun, Y. Teo, Kok Lay Bai, Y. |
| author_sort | Changjun, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method. |
| first_indexed | 2025-11-14T08:58:21Z |
| format | Journal Article |
| id | curtin-20.500.11937-39347 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:58:21Z |
| publishDate | 2013 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-393472017-09-13T15:33:38Z An exact penalty function method for nonlinear mixed discrete programming problems Changjun, Y. Teo, Kok Lay Bai, Y. exact penalty function nonlinear mixed integer programming In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method. 2013 Journal Article http://hdl.handle.net/20.500.11937/39347 10.1007/s11590-011-0391-2 Springer Verlag restricted |
| spellingShingle | exact penalty function nonlinear mixed integer programming Changjun, Y. Teo, Kok Lay Bai, Y. An exact penalty function method for nonlinear mixed discrete programming problems |
| title | An exact penalty function method for nonlinear mixed discrete programming problems |
| title_full | An exact penalty function method for nonlinear mixed discrete programming problems |
| title_fullStr | An exact penalty function method for nonlinear mixed discrete programming problems |
| title_full_unstemmed | An exact penalty function method for nonlinear mixed discrete programming problems |
| title_short | An exact penalty function method for nonlinear mixed discrete programming problems |
| title_sort | exact penalty function method for nonlinear mixed discrete programming problems |
| topic | exact penalty function nonlinear mixed integer programming |
| url | http://hdl.handle.net/20.500.11937/39347 |