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Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method
Author
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-10-27
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Jibrin, Shafiu. 2015. Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method. Journal of Mathematics،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1068683
Modern Language Association (MLA)
Jibrin, Shafiu. Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method. Journal of Mathematics No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1068683
American Medical Association (AMA)
Jibrin, Shafiu. Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method. Journal of Mathematics. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1068683
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068683