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Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities
Joint Authors
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-01-08
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
We give algorithms for solving the strict feasibility problem for linear matrix inequalities.
These algorithms are based on John Chinneck’s constraint consensus methods, in particular, the method of his original paper and the modified DBmax constraint consensus method from his paper with Ibrahim.
Our algorithms start with one of these methods as “Phase 1.” Constraint consensus methods work for any differentiable constraints, but we take advantage of the structure of linear matrix inequalities.
In particular, for linear matrix inequalities, the crossing points of each constraint boundary with the consensus ray can be calculated.
In this way we check for strictly feasible points in “Phase 2” of our algorithms.
We present four different algorithms, depending on whether the original (basic) or DBmax constraint consensus vector is used in Phase 1 and, independently, in Phase 2.
We present results of numerical experiments that compare the four algorithms.
The evidence suggests that one of our algorithms is the best, although none of them are guaranteed to find a strictly feasible point after a given number of iterations.
We also give results of numerical experiments indicating that our best method compares favorably to a new variant of the method of alternating projections.
American Psychological Association (APA)
Jibrin, Shafiu& Swift, James W.. 2015. Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities. Journal of Optimization،Vol. 2015, no. 2015, pp.1-16.
https://search.emarefa.net/detail/BIM-1069911
Modern Language Association (MLA)
Jibrin, Shafiu& Swift, James W.. Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities. Journal of Optimization No. 2015 (2015), pp.1-16.
https://search.emarefa.net/detail/BIM-1069911
American Medical Association (AMA)
Jibrin, Shafiu& Swift, James W.. Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities. Journal of Optimization. 2015. Vol. 2015, no. 2015, pp.1-16.
https://search.emarefa.net/detail/BIM-1069911
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1069911