The Shadow-Vertex Algorithm

  • Karl Heinz Borgwardt
Part of the Algorithms and Combinatorics book series (AC, volume 1)


This chapter is to explain the algorithm which shall be analyzed. For our probabilistic analysis it is necessary to use a so-called dual interpretation. Most of the readers may not be familiar with that way to describe the procedure. Therefore we start with the commonly used and well-known primal interpretation. In Section 2 we repeat most of the arguments of Section 1 in the new interpretation. And in Section 3 we show how the algorithm (in dual representation) can be realized in a corresponding tableau-form. So it is clear that much of the material is of an expository nature and that a certain amount of repetitions will occur. But the often observed confusion of readers by the different interpretations may be avoided by this way.


Convex Cone Pivot Step Pivot Element Optimal Simplex Start Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Karl Heinz Borgwardt
    • 1
  1. 1.Institute of MathematicsUniversity of AugsburgAugsburgWest Germany

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