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The conjugate gradient technique for certain quadratic network problems

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  • Larry J. Leblanc

Abstract

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large‐scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum‐cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.

Suggested Citation

  • Larry J. Leblanc, 1976. "The conjugate gradient technique for certain quadratic network problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(4), pages 597-602, December.
    • Handle: RePEc:wly:navlog:v:23:y:1976:i:4:p:597-602
    DOI: 10.1002/nav.3800230403
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