Generalized Linear Programming Solves the Dual
The generalized linear programming algorithm allows an arbitrary mathematical programming minimization problem to be analyzed as a sequence of linear programming approximations. Under fairly general assumptions, it is demonstrated that any limit point of the sequence of optimal linear programming du...
| Main Authors: | , , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5346 |
| _version_ | 1826215943818182656 |
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| author | Magnanti, Thomas L. Shapiro, Jeremy F., 1939- Wagner, Michael H. |
| author_facet | Magnanti, Thomas L. Shapiro, Jeremy F., 1939- Wagner, Michael H. |
| author_sort | Magnanti, Thomas L. |
| collection | MIT |
| description | The generalized linear programming algorithm allows an arbitrary mathematical programming minimization problem to be analyzed as a sequence of linear programming approximations. Under fairly general assumptions, it is demonstrated that any limit point of the sequence of optimal linear programming dual prices produced by the algorithm is optimal in a concave maximization problem that is dual to the arbitrary primal problem. This result holds even if the generalized linear programming problem does not solve the primal problem. The result is a consequence of the equivalence that exists between the operations of convexification and dualization of a primal problem. The exact mathematical nature of this equivalence is given. |
| first_indexed | 2024-09-23T16:39:56Z |
| format | Working Paper |
| id | mit-1721.1/5346 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:39:56Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/53462019-04-10T10:36:08Z Generalized Linear Programming Solves the Dual Magnanti, Thomas L. Shapiro, Jeremy F., 1939- Wagner, Michael H. The generalized linear programming algorithm allows an arbitrary mathematical programming minimization problem to be analyzed as a sequence of linear programming approximations. Under fairly general assumptions, it is demonstrated that any limit point of the sequence of optimal linear programming dual prices produced by the algorithm is optimal in a concave maximization problem that is dual to the arbitrary primal problem. This result holds even if the generalized linear programming problem does not solve the primal problem. The result is a consequence of the equivalence that exists between the operations of convexification and dualization of a primal problem. The exact mathematical nature of this equivalence is given. Supported in prt by the U.S. Army Research Office (Durham) under contract DAHC04-73-C-0032. 2004-05-28T19:34:54Z 2004-05-28T19:34:54Z 1973-09 Working Paper http://hdl.handle.net/1721.1/5346 en_US Operations Research Center Working Paper;OR 019-73 1746 bytes 1852887 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Magnanti, Thomas L. Shapiro, Jeremy F., 1939- Wagner, Michael H. Generalized Linear Programming Solves the Dual |
| title | Generalized Linear Programming Solves the Dual |
| title_full | Generalized Linear Programming Solves the Dual |
| title_fullStr | Generalized Linear Programming Solves the Dual |
| title_full_unstemmed | Generalized Linear Programming Solves the Dual |
| title_short | Generalized Linear Programming Solves the Dual |
| title_sort | generalized linear programming solves the dual |
| url | http://hdl.handle.net/1721.1/5346 |
| work_keys_str_mv | AT magnantithomasl generalizedlinearprogrammingsolvesthedual AT shapirojeremyf1939 generalizedlinearprogrammingsolvesthedual AT wagnermichaelh generalizedlinearprogrammingsolvesthedual |