Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method
We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be...
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| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/456392 |
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| author | Shafiu Jibrin |
| author_facet | Shafiu Jibrin |
| author_sort | Shafiu Jibrin |
| collection | DOAJ |
| description | We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem by using Infeasible Newton’s method applied to the KKT system of equations which can be started from any point. We implement the method using backtracking line search technique and also study the effect of large weights on the method. We use numerical experiments to compare Infeasible Newton’s method with Standard Newton’s method. The results show that Infeasible Newton’s method moves in the interior of the feasible regions often very quickly, starting from any point. We recommend it as a method for finding an interior point by setting each weight to be 1. It appears to work better than Standard Newton’s method in finding the weighted analytic center when none of weights is very large relative to the other weights. However, we find that Infeasible Newton’s method is more sensitive than Standard Newton’s method to large variation in the weights. |
| format | Article |
| id | doaj-art-8a0b21d9fc614ac3b56b482c8d054d94 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8a0b21d9fc614ac3b56b482c8d054d942025-02-03T01:31:09ZengWileyJournal of Mathematics2314-46292314-47852015-01-01201510.1155/2015/456392456392Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s MethodShafiu Jibrin0Department of Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ 86011-5717, USAWe study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem by using Infeasible Newton’s method applied to the KKT system of equations which can be started from any point. We implement the method using backtracking line search technique and also study the effect of large weights on the method. We use numerical experiments to compare Infeasible Newton’s method with Standard Newton’s method. The results show that Infeasible Newton’s method moves in the interior of the feasible regions often very quickly, starting from any point. We recommend it as a method for finding an interior point by setting each weight to be 1. It appears to work better than Standard Newton’s method in finding the weighted analytic center when none of weights is very large relative to the other weights. However, we find that Infeasible Newton’s method is more sensitive than Standard Newton’s method to large variation in the weights.http://dx.doi.org/10.1155/2015/456392 |
| spellingShingle | Shafiu Jibrin Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method Journal of Mathematics |
| title | Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method |
| title_full | Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method |
| title_fullStr | Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method |
| title_full_unstemmed | Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method |
| title_short | Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method |
| title_sort | computing weighted analytic center for linear matrix inequalities using infeasible newton s method |
| url | http://dx.doi.org/10.1155/2015/456392 |
| work_keys_str_mv | AT shafiujibrin computingweightedanalyticcenterforlinearmatrixinequalitiesusinginfeasiblenewtonsmethod |