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Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System

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Infinite Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 259))

Summary

In the first part of this paper, some consequences of the semi-infinite Motzkin alternative theorem are given. In particular, a refinement of an important result of Duffin, Jeroslow and Karlovitz, characterizing those sets which generate a closed convex cone, is obtained. In the second part, we apply these results to supply different sufficient conditions for the Farkas-Minkowski property of a semi-infinite linear system. Finally, by means of the methodology introduced in the paper, an application to the regularization of the linear semi-infinite programming problem is given.

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References

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas — Facultad de Ciencias, Universidad de Alicante, Spain, France

    M. A. Goberna & M. A. López

Authors
  1. M. A. Goberna
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  2. M. A. López
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Editor information

Editors and Affiliations

  1. Management Studies Group Engineering Department, Cambridge University, Mill Lane, Cambridge, CB2 1RX, UK

    Edward J. Anderson  & Andrew B. Philpott  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Goberna, M.A., López, M.A. (1985). Conditions for the Closedness of the Characteristic Cone Associated with an Infinite Linear System. In: Anderson, E.J., Philpott, A.B. (eds) Infinite Programming. Lecture Notes in Economics and Mathematical Systems, vol 259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46564-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-46564-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15996-4

  • Online ISBN: 978-3-642-46564-2

  • eBook Packages: Springer Book Archive

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