A Linear Approximation Approach to Duality in Nonlinear Programming
Linear approximation and linear programming duality theory are used as unifying tools to develop saddlepoint, Fenchel and local duality theory. Among results presented is a new and elementary proof of the necessity and sufficiency of the stability condition for saddlepoint duality, an equivalence be...
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| Format: | Working Paper |
| Language: | en_US |
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Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5344 |
| _version_ | 1811081626778599424 |
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| author | Magnanti, Thomas L. |
| author_facet | Magnanti, Thomas L. |
| author_sort | Magnanti, Thomas L. |
| collection | MIT |
| description | Linear approximation and linear programming duality theory are used as unifying tools to develop saddlepoint, Fenchel and local duality theory. Among results presented is a new and elementary proof of the necessity and sufficiency of the stability condition for saddlepoint duality, an equivalence between the saddlepoint and Fenchel theories, and nasc for an optimal solution of an optimization problem to be a Kuhn-Tucker point. Several of the classic "constraint qualifications" are discussed with respect to this last condition. In addition, generalized versions of Fenchel and Rockafeller duals are introduced. Finally, a shortened proof is given of a result of Mangasarian and Fromowitz that under fairly general conditions an optimal point is also a Fritz John point. |
| first_indexed | 2024-09-23T11:49:46Z |
| format | Working Paper |
| id | mit-1721.1/5344 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:49:46Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/53442019-04-12T08:17:18Z A Linear Approximation Approach to Duality in Nonlinear Programming Magnanti, Thomas L. Linear approximation and linear programming duality theory are used as unifying tools to develop saddlepoint, Fenchel and local duality theory. Among results presented is a new and elementary proof of the necessity and sufficiency of the stability condition for saddlepoint duality, an equivalence between the saddlepoint and Fenchel theories, and nasc for an optimal solution of an optimization problem to be a Kuhn-Tucker point. Several of the classic "constraint qualifications" are discussed with respect to this last condition. In addition, generalized versions of Fenchel and Rockafeller duals are introduced. Finally, a shortened proof is given of a result of Mangasarian and Fromowitz that under fairly general conditions an optimal point is also a Fritz John point. Supported in part by the US Army Research Office (Durham) under Contract DAHC04-70-C-0058 2004-05-28T19:34:47Z 2004-05-28T19:34:47Z 1973-04 Working Paper http://hdl.handle.net/1721.1/5344 en_US Operations Research Center Working Paper;OR 016-73 1746 bytes 1819696 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Magnanti, Thomas L. A Linear Approximation Approach to Duality in Nonlinear Programming |
| title | A Linear Approximation Approach to Duality in Nonlinear Programming |
| title_full | A Linear Approximation Approach to Duality in Nonlinear Programming |
| title_fullStr | A Linear Approximation Approach to Duality in Nonlinear Programming |
| title_full_unstemmed | A Linear Approximation Approach to Duality in Nonlinear Programming |
| title_short | A Linear Approximation Approach to Duality in Nonlinear Programming |
| title_sort | linear approximation approach to duality in nonlinear programming |
| url | http://hdl.handle.net/1721.1/5344 |
| work_keys_str_mv | AT magnantithomasl alinearapproximationapproachtodualityinnonlinearprogramming AT magnantithomasl linearapproximationapproachtodualityinnonlinearprogramming |