Abstract
Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computation time grows faster than linear as the size increases. There are also storage requirements. So, it is of interest to consider how to identify redundant constraints from a semidefinite programming problem. However, it is known that the problem of determining whether or not a linear matrix inequality constraint is redundant or not is NP complete, in general. In this paper, we develop deterministic methods for identifying all redundant linear constraints in semidefinite programming. We use a characterization of the normal cone at a boundary point and semidefinite programming duality. Our methods extend certain redundancy techniques from linear programming to semidefinite programming.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 601-617 |
| Number of pages | 17 |
| Journal | Journal of Interdisciplinary Mathematics |
| Volume | 10 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2007 |
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Keywords
- Linear matrix inequalities
- Normal cone
- Redundancy
- Semidefinite programming
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Identifying redundant linear constraints in systems of linear matrix inequality constraints. / Jibrin, Shafiu; Stover, Daniel.
In: Journal of Interdisciplinary Mathematics, Vol. 10, No. 5, 2007, p. 601-617.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Identifying redundant linear constraints in systems of linear matrix inequality constraints
AU - Jibrin, Shafiu
AU - Stover, Daniel
PY - 2007
Y1 - 2007
N2 - Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computation time grows faster than linear as the size increases. There are also storage requirements. So, it is of interest to consider how to identify redundant constraints from a semidefinite programming problem. However, it is known that the problem of determining whether or not a linear matrix inequality constraint is redundant or not is NP complete, in general. In this paper, we develop deterministic methods for identifying all redundant linear constraints in semidefinite programming. We use a characterization of the normal cone at a boundary point and semidefinite programming duality. Our methods extend certain redundancy techniques from linear programming to semidefinite programming.
AB - Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computation time grows faster than linear as the size increases. There are also storage requirements. So, it is of interest to consider how to identify redundant constraints from a semidefinite programming problem. However, it is known that the problem of determining whether or not a linear matrix inequality constraint is redundant or not is NP complete, in general. In this paper, we develop deterministic methods for identifying all redundant linear constraints in semidefinite programming. We use a characterization of the normal cone at a boundary point and semidefinite programming duality. Our methods extend certain redundancy techniques from linear programming to semidefinite programming.
KW - Linear matrix inequalities
KW - Normal cone
KW - Redundancy
KW - Semidefinite programming
UR - http://www.scopus.com/inward/record.url?scp=84890073978&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84890073978&partnerID=8YFLogxK
U2 - 10.1080/09720502.2007.10700521
DO - 10.1080/09720502.2007.10700521
M3 - Article
AN - SCOPUS:84890073978
VL - 10
SP - 601
EP - 617
JO - Journal of Interdisciplinary Mathematics
JF - Journal of Interdisciplinary Mathematics
SN - 0972-0502
IS - 5
ER -