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On Redundancy In Systems Of Linear Inequalities

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  • Telgen, Jan

Abstract

In this paper the concept of redundancy in systems of linear inequalities is established from the existence of the minimal inequality representation of a system of linear constraints. It is shown that absence of redundancy is a necessary and sufficient condition for having a minimal inequality representation of the system; then a minimal inequality representation can be obtained by deleting redundant constraints. Furthermore a general method to determine redundancy is developed; this method is based on the simplex method and is greatly inspired by Gal [2]. A number of known methods can be shown to be simplified variants of this method. Finally the equivalence, in terms of complexity theory, of the problem of determining redundancy and the general linear programming problem, is proved. From this a class of problems is indicated, for which it may be fruitful to determine redundancy.

Suggested Citation

  • Telgen, Jan, 1977. "On Redundancy In Systems Of Linear Inequalities," Econometric Institute Archives 272154, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272154
    DOI: 10.22004/ag.econ.272154
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    References listed on IDEAS

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    1. Jansen, R. & Louter, A. S., 1977. "An Efficient Way Of Programming Eaves' Fixed Point Algorithm," Econometric Institute Archives 272150, Erasmus University Rotterdam.
    2. Telgen, J., 1977. "On R.W. Llewellyn'S Rules To Identify Redundant Constraints; A Detailed Critique And Some Generalizations," Econometric Institute Archives 272155, Erasmus University Rotterdam.
    3. Hazewinkel, M., 1977. "Twisted Lubin-Tate Formal Group Laws, Ramified Witt Vectors And (Ramified) Artin-Hasse Exponentials," Econometric Institute Archives 272149, Erasmus University Rotterdam.
    4. Hazewinkel, M., 1977. "Degenerating Families Of Linear Dynamical Systems I," Econometric Institute Archives 272148, Erasmus University Rotterdam.
    5. Telgen, Jan, 1977. "Redundant And Non-Binding Constraints In Linear Programming Problems," Econometric Institute Archives 272156, Erasmus University Rotterdam.
    6. Stroeker, R. J., 1977. "Application Of Non-Linear Programming To Plane Geometry," Econometric Institute Archives 272152, Erasmus University Rotterdam.
    7. de Haan, L. & Ridder, G., 1977. "Stochastic Compactness Of Sample Extremes," Econometric Institute Archives 272153, Erasmus University Rotterdam.
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    2. Hazewinkel, M., 1979. "On Families Of Linear Systems: Degenerating Phenomena," Econometric Institute Archives 272182, Erasmus University Rotterdam.

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