A Method to Solve the Neighbourhood Problem

  • H.-J. Kruse
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 260)


This chapter deals with a special degeneracy problem, namely the problem of determining all neighbouring vertices of a degenerate vertex of a convex polytope. In the following we call it the neighbourhood problem. The determination of all neighbouring vertices of a nondegenerate vertex is unproblematic, since a nondegenerate vertex has exactly one pivot tableau and all neighbouring vertices can be determined on the basis of this tableau in one pivot step each time. In contrast to this, a degenerate vertex xo is associated with different pivot tableaux, and in exceptional cases only can all neighbouring vertices be computed using just one pivot tableau of xo 1).


Linear Programming Problem Tree Node Neighbouring Vertex Neighbourhood Problem Basic Feasible Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • H.-J. Kruse
    • 1
  1. 1.Fachbereich WirtschaftswissenschaftFernuniversität HagenHagen 1Germany

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