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Degeneracy graphs

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Encyclopedia of Operations Research and Management Science

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INTRODUCTION

For a given linear-programming problem, primal degeneracy means that a basic feasible solution has at least one basic variable equal to zero. The problem is dual degenerate if a nonbasic variable has its reduced cost equal to zero (the condition for a multiple optimal solution to exist). Primal degeneracy may arise when there are some (weakly) redundant constraints (Karwan et al., 1983) or the structure of the corresponding convex polyhedral feasible set causes an extreme point to become overdetermined.

In nonlinear programming, such points are sometimes called singularities (Guddat et al., 1990). Here, constraint redundancy is equivalent to the failure of the linear independence constraint qualification of the binding constraint gradients, which, in general, leads to the nonuniqueness of optimal Lagrange multipliers (Fiacco and Liu, 1993).

We focus here on primal degeneracy in the linear case: it is associated with multiple optimal bases and it allows for basis cycling to...

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References

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Author information

Authors and Affiliations

  1. Fern Universität, Hagen, Germany

    Tomas Gal

Authors
  1. Tomas Gal
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Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

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© 2001 Kluwer Academic Publishers

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Gal, T. (2001). Degeneracy graphs . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_224

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  • DOI: https://doi.org/10.1007/1-4020-0611-X_224

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-7923-7827-3

  • Online ISBN: 978-1-4020-0611-1

  • eBook Packages: Springer Book Archive

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