Mathematical Programming

, Volume 6, Issue 1, pp 62–88 | Cite as

Validation of subgradient optimization

  • Michael Held
  • Philip Wolfe
  • Harlan P. Crowder


The “relaxation” procedure introduced by Held and Karp for approximately solving a large linear programming problem related to the traveling-salesman problem is refined and studied experimentally on several classes of specially structured large-scale linear programming problems, and results on the use of the procedure for obtaining exact solutions are given. It is concluded that the method shows promise for large-scale linear programming


Exact Solution Mathematical Method Programming Problem Linear Programming Problem Subgradient Optimization 
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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Copyright information

© The Mathematical Programming Society 1974

Authors and Affiliations

  • Michael Held
    • 1
  • Philip Wolfe
    • 2
  • Harlan P. Crowder
    • 2
  1. 1.IBM Systems Research InstituteNew YorkUSA
  2. 2.IBM Watson Research CenterYorktown HeightsUSA

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