Constraint Consensus Methods for Finding Strictly Feasible Points of Linear Matrix Inequalities

Shafiu Jibrin and James W. Swift

Journal of Optimization, 2015, vol. 2015, 1-16

Abstract:

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.

Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/7179/2015/790451.pdf (application/pdf)
http://downloads.hindawi.com/journals/7179/2015/790451.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjopti:790451

DOI: 10.1155/2015/790451

Access Statistics for this article

More articles in Journal of Optimization from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().