Annals of Operations Research

, Volume 22, Issue 1, pp 23–41 | Cite as

Parallel solution of large-scale, block-angular linear programs

  • J. B. Rosen
  • Robert S. Maier


Many important large-scale optimization problems can be formulated as linear programs with a block-angular structure. This structure lends itself naturally to parallel solutions and is used to great advantage in the solution method described. To demonstrate the efficiency of the method, it has been implemented and computationally tested on both a shared-memory vector multiprocessor (CRAY-2) and a local-memory hypercube (NCUBE/seven) with 64 processors. Computational results for problems with as many as 24,000 rows and 74,000 columns (1,024 blocks and 1.4 million nonzero elements) are presented. A problem of this size was solved on the NCUBE in less than four minutes and the CRAY-2 in 37 seconds.


Computational Result Solution Method Nonzero Element Parallel Solution Vector Multiprocessor 
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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  1. [1]
    W.J. Carolan et al., An empirical evaluation of the KORBX algorithms for military airlift applications, Technical Report 89-OR-86, CINCMAC Analysis Group, Scott AFB, Illinois (1989).Google Scholar
  2. [2]
    J.L. Gustavson, G.R. Montry and R.E. Benner, Development of parallel methods for a 1024-processor hypercube, SIAM J. Sci. Stat. Computing 9(1988)609–638.CrossRefGoogle Scholar
  3. [3]
    J. Ho and E. Loute, Computational experience with advanced implementation of decomposition algorithms for linear programming, Math. Progr. 27(1983)283–290.Google Scholar
  4. [4]
    L.S. Lasdon,Optimization Theory for Large Systems (Macmillan, London, 1970).Google Scholar
  5. [5]
    R.S. Maier, Parallel solution of large-scale structured optimization problems, Ph.D. Dissertation, University of Minnesota (1989).Google Scholar
  6. [6]
    D. Medhi, Parallel bundle-based decomposition for large-scale structured mathematical programming problems, Ann. Oper. Res., this volume.Google Scholar
  7. [7]
    K. Murty,Linear Programming (Wiley, New York, 1983).Google Scholar
  8. [8]
    J.B. Rosen, Primal partition programming for block diagonal matrices, Numerische Mathematik 6(1964)250–260.CrossRefGoogle Scholar
  9. [9]
    R.J.-B. Wets,Numerical Techniques for Stochastic Optimization (Springer-Verlag, Berlin, 1988).Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1990

Authors and Affiliations

  • J. B. Rosen
    • 1
  • Robert S. Maier
    • 1
  1. 1.Computer Science DepartmentUniversity of MinnesotaMinneapolisUSA

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