K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau

References

  • Andersen K., Cornuéjols G., Li Y. Improving cuts in integer programming. (2001) INFORMS Annual ConferenceMiami Beach http://www.informs.org/Conf/Miami2001/TALKS/TC11.htmlGoogle Scholar
  • Balas E., Ceria S., Cornuéjols G., Natraj N. Gomory cuts revisited. Oper. Res. Lett. (1996) 19:1–9CrossrefGoogle Scholar
  • Bowman V., Nemhauser G. A finite proof for modified Dantzig cuts in integer programming. Naval Res. Logist. Quart. (1970) 17:309–313CrossrefGoogle Scholar
  • Ceria S., Cornuéjols G., Dawande M., Balas E., Clausen J. Optimizing generalized Gomory cuts for pure and mixed integer programs. Lecture Notes in Computer Science (1995) No. 920Google Scholar
  • Chvátal V. Edmonds polytope and a hierarchy of combinatorial problems. Discrete Math (1973) 4:305–337CrossrefGoogle Scholar
  • Dawande M. (2000) . Private communicationGoogle Scholar
  • Garfinkel R., Nemhauser G.Integer Programming (1972) (Wiley, New York) Google Scholar
  • Glover F. Generalized cuts in Diophantine programming. Management Sci (1966) 13:254–268LinkGoogle Scholar
  • Gomory R. Outline of an algorithm for integer solutions to linear programs. Bull. Amer. Math. Soc. (1958) 64:275–278CrossrefGoogle Scholar
  • Gomory R., Bellman R. E., Hall M. Solving linear programming problems in integers. Combinatorial Analysis (1960) (American Mathematical Society, Providence, RI) 211–216CrossrefGoogle Scholar
  • Gomory R., Graves R., Wolfs P. An algorithm for integer solutions to linear programs. Recent Advances in Mathematical Programming (1963) (McGraw-Hill, New York) 269–302Google Scholar
  • Gomory R. Some polyhedra related to combinatorial problems. Linear Algebra and Its Applications (1969) 2:451–558CrossrefGoogle Scholar
  • Gomory R. Corner polyhedra and their connection with cutting planes. (1999) . Integer Programming Symposium, IBM T.J. Watson Research Center, Yorktown Heights, NYGoogle Scholar
  • Gomory R., Hoffman A. On the convergence of an integer programming process. Naval Res. Logist. Quart. (1963) 10:121–124CrossrefGoogle Scholar
  • Gomory R., Johnson E. Some continuous functions related to corner polyhedra, Part I. Math. Programming (1972a) 3:23–85CrossrefGoogle Scholar
  • Gomory R., Johnson E. Some continuous functions related to corner polyhedra, Part II. Math. Programming (1972b) 3:359–389CrossrefGoogle Scholar
  • Günlük O., Pochet Y. Mixing mixed-integer inequalities. Math. Programming A (2001) 90:429–457CrossrefGoogle Scholar
  • Johnson E. On the group problem for mixed integer programming. Math. Programming Stud. (1974) 2:137–179CrossrefGoogle Scholar
  • Marchand H., Wolsey L. Aggregation and mixed integer rounding to solve MIPs. Oper. Res. (2001) 49:363–371LinkGoogle Scholar
  • Martello S., Toth P.Knapsack Problems: Algorithms and Computer Implementations (1989) (Wiley, New York) Google Scholar
  • Martin G., Graves R., Wolfs P. An accelerated Euclidean algorithm for integer linear programming. Recent Adv. in Math. Programming (1963) (McGraw-Hill, New York) Google Scholar
  • Miliotis P. Using cutting planes to solve the symmetric traveling salesman problem. Math. Programming (1978) 15:177–188CrossrefGoogle Scholar
  • Schrijver A.Theory of Linear and Integer Programming (1986) (Wiley, New York) Google Scholar
  • Vizvári B. Two algorithms to get strong Gomory cuts. Optimization (1989) 20:117–126CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.