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Decomposed enumeration of extreme points in the linear programming problem

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Abstract

In this paper we consider the problem of enumeration of extreme points in the linear programming problem when the matrix is of block-angular type. It is shown how decomposition methods can be used. Finally application of decomposed enumeration to the problem of computing equilibrium prices in a capital market network is given as an example.

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References

  1. M. Boyer, S. Storøy and S. Thore:Equilibrium Returns in Capital Market Networks, paper to The European Meeting of The Econometric Society, Budapest, 1972.

  2. G. Dahl and S. Storøy:Enumeration of Vertices in The Linear Programming Problem, Report no. 45, Dept. of Applied Mathematics, University of Bergen, 1973.

  3. H. Müller-Mehrbach:Upper-Bounding-Technique, Generalized Upper-Bounding-Technique and Direct Decomposition in Linear Programming, in Decomposition of Large Scale Systems, editor: D. Himmelblau, North Holland Publ. Comp., Amsterdam, 1973.

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  4. S. Storøy:An Algorithm for Finding a Vector in The Intersection of Open Convex Polyhedral Cones, BIT 13 (1973) 114–119.

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Authors and Affiliations

  1. Edb-Avdelingen, Universitetet I Bergen, H. Fossgt. 6, Bergen, Norway

    Grete Dahl & Sverre Storøy

  2. Matematisk Institutt, Universitetet I Bergen, Allégt. 53-55, Bergen, Norway

    Grete Dahl & Sverre Storøy

Authors
  1. Grete Dahl
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  2. Sverre Storøy
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Dahl, G., Storøy, S. Decomposed enumeration of extreme points in the linear programming problem. BIT 15, 151–157 (1975). https://doi.org/10.1007/BF01932688

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  • DOI: https://doi.org/10.1007/BF01932688

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