Monte Carlo Algorithms for the Detection of Necessary Linear Matrix Inequality Constraints

Shafiu Jibrin, Irwin S. Pressman

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor.

Original languageEnglish (US)
Pages (from-to)139-153
Number of pages15
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Volume2
Issue number2
StatePublished - 2001

Fingerprint

Monte Carlo Algorithm
Semidefinite Programming
Inequality Constraints
programming
Linear matrix inequalities
Matrix Inequality
Linear Inequalities
Necessary
Linear programming
linear programming
Monte Carlo Techniques
Demonstrate

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Mechanics of Materials
  • Applied Mathematics
  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

@article{902bd6162f7d402eb0a779b726dfadd2,
title = "Monte Carlo Algorithms for the Detection of Necessary Linear Matrix Inequality Constraints",
abstract = "We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor.",
author = "Shafiu Jibrin and Pressman, {Irwin S.}",
year = "2001",
language = "English (US)",
volume = "2",
pages = "139--153",
journal = "International Journal of Nonlinear Sciences and Numerical Simulation",
issn = "1565-1339",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "2",

}

TY - JOUR

T1 - Monte Carlo Algorithms for the Detection of Necessary Linear Matrix Inequality Constraints

AU - Jibrin, Shafiu

AU - Pressman, Irwin S.

PY - 2001

Y1 - 2001

N2 - We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor.

AB - We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor.

UR - http://www.scopus.com/inward/record.url?scp=0035639647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035639647&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035639647

VL - 2

SP - 139

EP - 153

JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

SN - 1565-1339

IS - 2

ER -