Averaging Schemes for Solving Fived Point and Variational Inequality Problems
We develop and study averaging schemes for solving fixed point and variational inequality problems. Typically, researchers have established convergence results for solution methods for these problems by establishing contractive estimates for their algorithmic maps. In this paper, we establish global...
| Main Authors: | , |
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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/1721.1/5325 |
| _version_ | 1826216745622306816 |
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| author | Magnanti, Thomas L. Perakis, Georgia |
| author_facet | Magnanti, Thomas L. Perakis, Georgia |
| author_sort | Magnanti, Thomas L. |
| collection | MIT |
| description | We develop and study averaging schemes for solving fixed point and variational inequality problems. Typically, researchers have established convergence results for solution methods for these problems by establishing contractive estimates for their algorithmic maps. In this paper, we establish global convergence results using nonexpansive estimates. After first establishing convergence for a general iterative scheme for computing fixed points, we consider applications to projection and relaxation algorithms for solving variational inequality problems and to a generalized steepest descent method for solving systems of equations. As part of our development, we also establish a new interpretation of a norm condition typically used for establishing convergence of linearization schemes, by associating it with a strong-f-monotonicity condition. We conclude by applying our results to transportation networks. |
| first_indexed | 2024-09-23T16:52:44Z |
| format | Working Paper |
| id | mit-1721.1/5325 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:52:44Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/53252019-04-12T08:16:20Z Averaging Schemes for Solving Fived Point and Variational Inequality Problems Magnanti, Thomas L. Perakis, Georgia We develop and study averaging schemes for solving fixed point and variational inequality problems. Typically, researchers have established convergence results for solution methods for these problems by establishing contractive estimates for their algorithmic maps. In this paper, we establish global convergence results using nonexpansive estimates. After first establishing convergence for a general iterative scheme for computing fixed points, we consider applications to projection and relaxation algorithms for solving variational inequality problems and to a generalized steepest descent method for solving systems of equations. As part of our development, we also establish a new interpretation of a norm condition typically used for establishing convergence of linearization schemes, by associating it with a strong-f-monotonicity condition. We conclude by applying our results to transportation networks. 2004-05-28T19:33:50Z 2004-05-28T19:33:50Z 1994-07 Working Paper http://hdl.handle.net/1721.1/5325 en_US Operations Research Center Working Paper;OR 296-94 2370284 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Magnanti, Thomas L. Perakis, Georgia Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title | Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title_full | Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title_fullStr | Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title_full_unstemmed | Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title_short | Averaging Schemes for Solving Fived Point and Variational Inequality Problems |
| title_sort | averaging schemes for solving fived point and variational inequality problems |
| url | http://hdl.handle.net/1721.1/5325 |
| work_keys_str_mv | AT magnantithomasl averagingschemesforsolvingfivedpointandvariationalinequalityproblems AT perakisgeorgia averagingschemesforsolvingfivedpointandvariationalinequalityproblems |