Duality Based Characterizations of Efficient Facets
Most practical applications of multicriteria decision making can be formulated in terms of efficient points determined by preference cones with polyhedral closure. Using linear approximations and duality from mathematical programming, we characterize a family of supporting hyperplanes that define th...
| Main Authors: | , |
|---|---|
| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
|
| Online Access: | http://hdl.handle.net/1721.1/5162 |
| _version_ | 1826216211107545088 |
|---|---|
| author | Bitran, Gabriel R. Magnanti, Thomas L. |
| author_facet | Bitran, Gabriel R. Magnanti, Thomas L. |
| author_sort | Bitran, Gabriel R. |
| collection | MIT |
| description | Most practical applications of multicriteria decision making can be formulated in terms of efficient points determined by preference cones with polyhedral closure. Using linear approximations and duality from mathematical programming, we characterize a family of supporting hyperplanes that define the efficient facets of a set of alternatives with respect to such preference cones. We show that a subset of these hyperplanes generate maximal efficient facets. These characterizations permit us to devise a new algorithm for generating all maximal efficient facets of multicriteria optimization problems with polyhedral structure. |
| first_indexed | 2024-09-23T16:43:46Z |
| format | Working Paper |
| id | mit-1721.1/5162 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:43:46Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/51622019-04-12T08:06:52Z Duality Based Characterizations of Efficient Facets Bitran, Gabriel R. Magnanti, Thomas L. Most practical applications of multicriteria decision making can be formulated in terms of efficient points determined by preference cones with polyhedral closure. Using linear approximations and duality from mathematical programming, we characterize a family of supporting hyperplanes that define the efficient facets of a set of alternatives with respect to such preference cones. We show that a subset of these hyperplanes generate maximal efficient facets. These characterizations permit us to devise a new algorithm for generating all maximal efficient facets of multicriteria optimization problems with polyhedral structure. Supported in part by the National Science Foundation grant MCS77-24654. Supported in part by the Army Research Office (Durham) contract DAAG29-76-C-0064. 2004-05-28T19:25:54Z 2004-05-28T19:25:54Z 1979-10 Working Paper http://hdl.handle.net/1721.1/5162 en_US Operations Research Center Working Paper;OR 092-79 1746 bytes 1234775 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Bitran, Gabriel R. Magnanti, Thomas L. Duality Based Characterizations of Efficient Facets |
| title | Duality Based Characterizations of Efficient Facets |
| title_full | Duality Based Characterizations of Efficient Facets |
| title_fullStr | Duality Based Characterizations of Efficient Facets |
| title_full_unstemmed | Duality Based Characterizations of Efficient Facets |
| title_short | Duality Based Characterizations of Efficient Facets |
| title_sort | duality based characterizations of efficient facets |
| url | http://hdl.handle.net/1721.1/5162 |
| work_keys_str_mv | AT bitrangabrielr dualitybasedcharacterizationsofefficientfacets AT magnantithomasl dualitybasedcharacterizationsofefficientfacets |