Skip to main content
SpringerLink
Log in
Book cover

System Modelling and Optimization pp 241–250Cite as

The interior point method for LP on parallel computers

  • II Mathematical Programming
  • Conference paper
  • First Online:

  • 124 Accesses

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 180))

Abstract

In this paper we describe a unified algorithmic framework for the interior point method (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is important.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Karmarkar N., A New Polynomial Time Algorithm For Linear Programming, Combinatorica, vol 4,pp 373–379, 1984

    Article  MATH  MathSciNet  Google Scholar 

  2. Lustig J. I., Marsten E. R.,Shanno D.F., On Implementing Mehrotra’s Predictor-Corrector Interior Point Method For Linear Programming, Technical Report SOR 90-03, Department of Civil Engineering and Operational Research, Princeton University, 1990

    Google Scholar 

  3. Bixby R.E., Gregory J.W.,Lustig I.J.,Marsten R.E.,Shanno D.F., Very Large Scale Linear Programming: A Case Study In Combining Interior Point And Simplex Methods, Department of Mathematical Science, Rice University, Texas, 1991

    Google Scholar 

  4. Andersen J., Levkovitz R., Mitra G., Tamiz M., Adapting IPM For The Solution Of LPs On Serial,Coarse Grain Parallel And Massively Parallel Computer, Brunel University, 1990.

    Google Scholar 

  5. George J.A., Liu J.W.,Computer Solution Of Large Sparse Positive Definite Systems, Prentice Hall,1981

    Google Scholar 

  6. Monteiro D.C., Adler I., Interior Path Following Primal-Dual Algorithm, Mathematical Programming 44, 1989

    Google Scholar 

  7. Megiddo N., On Finding Primal-Dual and Dual-Optimal Bases. ORSA Journal on Computing No2, Winter 1991.

    Google Scholar 

  8. Liu W. H., Reordering Sparse Matrices For Parallel Elimination, Parallel Computing, Volume 11, pp73–91, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  9. Andersen J.H.,Mitra G.,Parkinson D.,The Scheduling Of Sparse Matrix-Vector Multiplication On a Massively Parallel DAP Computer, Brunel University, 1991.

    Google Scholar 

  10. Golub J., Van-Loan C.F.,Matrix Computation, North Oxford Academic, 1983.

    Google Scholar 

  11. Lai C.H., Liddell H.M., Preconditioned Conjugate Gradient Methods On The DAP, Proceeding From The Mathematics Of Finite Elements & Applications, Vol 4. pp 147–156,1988

    Google Scholar 

  12. Mitra G.,Levkovitz R.,Tamiz M.,Integration Of IPM Within Simplex, Experiments In Feasible Basis Recovery, Brunel University, Presented to 14’th MPS Symposium,1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Brunel - The University Of West London, U.K.

    R. Levkovitz, J. Andersen & G. Mitra

Authors
  1. R. Levkovitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Andersen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

L. D. Davisson A. G. J. MacFarlane H. Kwakernaak J. L. Massey Ya Z. Tsypkin A. J. Viterbi Peter Kall

Rights and permissions

Reprints and permissions

Copyright information

© 1992 International Federation for Information Processing

About this paper

Cite this paper

Levkovitz, R., Andersen, J., Mitra, G. (1992). The interior point method for LP on parallel computers. In: Davisson, L.D., et al. System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113291

Download citation

  • DOI: https://doi.org/10.1007/BFb0113291

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55577-3

  • Online ISBN: 978-3-540-47220-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation