### 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 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Journal of Interdisciplinary Mathematics*, vol. 10, no. 5, pp. 601-617. https://doi.org/10.1080/09720502.2007.10700521

}

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

VL - 10

SP - 601

EP - 617

JO - Journal of Interdisciplinary Mathematics

JF - Journal of Interdisciplinary Mathematics

SN - 0972-0502

IS - 5

ER -