Gomory's method based on the objective equivalent face technique

  • Yan Zizong
  • Fei Pusheng
  • Wang Xiaoli


This paper discusses a re-examination of dual methods based on Gomory's cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.

Key words

integer programming Gomory's cutting plane dual gap primal and dual algorithm 

CLC number

O 221.4 


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  1. [1]
    Nemhauser G L, Wolsey L A.Integer and Combinationrial Optimization[M]. New York: Wiley, 1988.Google Scholar
  2. [2]
    Padberg M, Rinalfi G. A Branch-and-Cut Aldorithm for the Resolution of Large-scale Symmetric Travelling Salesman Problem[J].SIAM Review, 1991,33: 60–100.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Capprara A, Fischetti M. Branch-and-Cut Algorithms[C]// Dell's Amico M, Maffioli F, Martello S eds.Annotated Bibliographices in Combinatorial Optimization. New York: Wiley, 1997: 45–64.Google Scholar
  4. [4]
    Gomory R. Outline of An Algorithm for Integer Solution Programs[J].Bulletin of the AMS, 1958,64: 275–278.MATHMathSciNetGoogle Scholar
  5. [5]
    Padberg M. Classical Cuts for Mixed-Integer Programming and Branch-and-Cut[J].Math Meth Oper Res, 2001,53: 173–203.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Fletcher M. Numberical Experience with Lower Bound for MIQP Branch and Bound[J].SIAM Journal on Optimization, 1988,8: 604–616.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Haus D D, Köppe M, Weismantel R. The Integeral Basis Method for Integer Programming[J].Mathematical Methods of Operations Research, 2001,53: 353–361.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Sharma S, Sharma R. New Technique for Solving Primal All-Integer Linear Programming[J].Opsearch, 1997,34: 62–68.MATHMathSciNetGoogle Scholar
  9. [9]
    Urbaniak R, Weismatel R, Ziegler G. A Variant of Bucgberger's Algorithm for Integer Programming[J].SIAM Journal on Discrete Mathematic, 1997,1: 96–108.CrossRefGoogle Scholar
  10. [10]
    Yan Zizong, Fei Pusheng. Current Equivalent Face Algorithm for Linear Programming[J].Numer Math & Appl, 2005,1: 49–58.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhan, HubeiChina
  2. 2.School of Information and MathematicsYangtze UniversityJingzhou, HubeiChina

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