Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones
Optimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Ch...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2010/307209 |
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| _version_ | 1832566614462038016 |
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| author | Anna Weigandt Kaitlyn Tuthill Shafiu Jibrin |
| author_facet | Anna Weigandt Kaitlyn Tuthill Shafiu Jibrin |
| author_sort | Anna Weigandt |
| collection | DOAJ |
| description | Optimization problems with second-order cone constraints (SOCs) can be solved efficiently
by interior point methods. In order for some of these methods to get started or
to converge faster, it is important to have an initial feasible point or near-feasible point.
In this paper, we study and apply Chinneck's Original constraint consensus method and
DBmax constraint consensus method to find near-feasible points for systems of SOCs.
We also develop and implement a new backtracking-like line search technique on these
methods that attempts to increase the length of the consensus vector, at each iteration,
with the goal of finding interior feasible points. Our numerical results indicate that the
new methods are effective in finding interior feasible points for SOCs. |
| format | Article |
| id | doaj-art-5a874f11e18a49ccbf3294beef46aaa6 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5a874f11e18a49ccbf3294beef46aaa62025-02-03T01:03:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422010-01-01201010.1155/2010/307209307209Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order ConesAnna Weigandt0Kaitlyn Tuthill1Shafiu Jibrin2Department of Mathematics, Illinois State University, Normal, IL 61790-4520, USADepartment of Mathematics, Saint Michael's College, Colchester, VT 05439, USADepartment of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, USAOptimization problems with second-order cone constraints (SOCs) can be solved efficiently by interior point methods. In order for some of these methods to get started or to converge faster, it is important to have an initial feasible point or near-feasible point. In this paper, we study and apply Chinneck's Original constraint consensus method and DBmax constraint consensus method to find near-feasible points for systems of SOCs. We also develop and implement a new backtracking-like line search technique on these methods that attempts to increase the length of the consensus vector, at each iteration, with the goal of finding interior feasible points. Our numerical results indicate that the new methods are effective in finding interior feasible points for SOCs.http://dx.doi.org/10.1155/2010/307209 |
| spellingShingle | Anna Weigandt Kaitlyn Tuthill Shafiu Jibrin Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones Journal of Applied Mathematics |
| title | Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones |
| title_full | Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones |
| title_fullStr | Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones |
| title_full_unstemmed | Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones |
| title_short | Constraint Consensus Methods for Finding Interior Feasible Points in Second-Order Cones |
| title_sort | constraint consensus methods for finding interior feasible points in second order cones |
| url | http://dx.doi.org/10.1155/2010/307209 |
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