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Identifying Redundant Constraints and Implicit Equalities in Systems of Linear Constraints

Author

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  • Jan Telgen

    (Rabobank Nederland, Zeist, The Netherlands)

Abstract

Redundant constraints are constraints that can be omitted from a system of linear constraints without changing the feasible region. Implicit equalities are inequality constraints that can be replaced by equalities without changing the feasible region. We prove some theorems concerning the identification of both kinds of constraints. Based on these theorems two methods are developed that allow identification of all redundant constraints and all implicit equalities. Computational experience on small problems indicates a behavior at least competitive with other methods in this field.

Suggested Citation

  • Jan Telgen, 1983. "Identifying Redundant Constraints and Implicit Equalities in Systems of Linear Constraints," Management Science, INFORMS, vol. 29(10), pages 1209-1222, October.
    • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:10:p:1209-1222
    DOI: 10.1287/mnsc.29.10.1209
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    Cited by:

    1. Daalmans Jacco, 2018. "Constraint Simplification for Data Editing of Numerical Variables," Journal of Official Statistics, Sciendo, vol. 34(1), pages 27-39, March.
    2. Freixas, Josep & Kaniovski, Serguei, 2014. "The minimum sum representation as an index of voting power," European Journal of Operational Research, Elsevier, vol. 233(3), pages 739-748.
    3. Caron, Richard J. & Obuchowska, Wieslawa T., 1996. "Quadratically constrained convex quadratic programmes: faulty feasible regions," European Journal of Operational Research, Elsevier, vol. 94(1), pages 134-142, October.
    4. Obuchowska, Wieslawa T., 1998. "Infeasibility analysis for systems of quadratic convex inequalities," European Journal of Operational Research, Elsevier, vol. 107(3), pages 633-643, June.
    5. Liu, Yanwu & Tu, Yan & Zhang, Zhongzhen, 2021. "The row pivoting method for linear programming," Omega, Elsevier, vol. 100(C).
    6. Fan, Yanqin & Shi, Xuetao, 2023. "Wald, QLR, and score tests when parameters are subject to linear inequality constraints," Journal of Econometrics, Elsevier, vol. 235(2), pages 2005-2026.
    7. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.

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    Keywords

    programming: linear;

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