Skip to main content

Algorithms for some simple infinite dimensional linear programs

  • Theory And Applications Of Programming
  • Conference paper
  • First Online:
System Modeling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 38))

  • 327 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.J. ANDERSON, Basic solutions and a simplex method for a class of continuous linear programs, Optimization techniques, 9th IFIP Conference, Springer-Verlag, Berlin, 1980.

    Google Scholar 

  2. E.J.ANDERSON, P.NASH & A.B.PHILPOTT, A class of continuous network flow problems, internal technical report, CUED/F-CAMS/TR 214, 1981.

    Google Scholar 

  3. E.J.ANDERSON & A.B.PHILPOTT, Duality and an algorithm for a class of continuous transportation problems, in preparation.

    Google Scholar 

  4. P.APPELL, Le problème géométrique des déblais et remblais, Memorial des Sciènces Mathématiques, 1928.

    Google Scholar 

  5. R.BELLMAN, Dynamic Programming, Princeton University Press, 1957.

    Google Scholar 

  6. W.P. DREWS, R.J. HARTBERGER and R.G. SEGERS, A simplex-like algorithm for continuous-time linear optimal control problems, Optimisation methods in resource allocation, R.W. Cottle and J. Kraup, ed., Crane Russak and Co Inc., New York, 1974.

    Google Scholar 

  7. L.FORD & D.R.FULKERSON, Flows in Networks, Princeton University Press, 1962.

    Google Scholar 

  8. R. GRINOLD, Symmetric duality for a class of continuous linear programming problems, SIAM J. Appl. Math., 18 (1970), 84–97.

    Google Scholar 

  9. L.V. KANTOROVITCH, On the translocation of masses, Doklady Akad. Nauk.SSSR, 37 (1942), 199–201.

    Google Scholar 

  10. K.S. KRETSCHMER, Programmes in paired spaces, Canadian J. Math., 13 (1961), 323–334.

    Google Scholar 

  11. R.S.LEHMANN, On the continuous simplex method, RM-1386, Rand Corporation, 1954.

    Google Scholar 

  12. V.L. LEVIN & A.A. MILYUTIN, The problem of mass transfer with a discontinuous cost function, Russian Math. Surveys, 34 (1978), 1–78.

    Google Scholar 

  13. N. LEVINSON, A class of continuous linear programming problems, J. Math. Anal. and Appl., 16 (1966), 73–83.

    Google Scholar 

  14. G.MONGE, Mémoires de l'Académie des Sciènces, 1781.

    Google Scholar 

  15. T. NAKAMURA and M. YAMASAKI, Sufficient conditions for duality theorems in infinite linear programming problems, Hiroshima Math. J., 9 (1979), 323–334.

    Google Scholar 

  16. A.F.PEROLD, Fundamentals of a continuous time simplex method, Stanford University technical report, SOL 78-26, 1978.

    Google Scholar 

  17. G.STRANG, Maximal flow through a domain, to appear.

    Google Scholar 

  18. W.F. TYNDALL, An extended duality theory for continuous linear programming problems, SIAM J. Appl. Maths., 15 (1967), 1294–1298.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

R. F. Drenick F. Kozin

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Anderson, E.J., Philpott, A.B. (1982). Algorithms for some simple infinite dimensional linear programs. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006166

Download citation

  • DOI: https://doi.org/10.1007/BFb0006166

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11691-2

  • Online ISBN: 978-3-540-39459-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics