CglGMI

Gomory Mixed-Integer cuts with numerical safety testing

Algorithm

Slack Elimination (eliminateSlack): GMI from tableau uses slack variables; convert to original:

$$Substitute s_{i} = b_{i} - a_{i}'x using original constraint$$ Produces cut in terms of structural variables only.

Complexity: $O(nnz * log(maxdenom)$) for rational approximation

References:

  • Gomory (1960) - An algorithm for mixed-integer problems
  • Cornuéjols (2008) - Valid inequalities for MIP
  • Cook, Kannan, Schrijver (1990) - Chvátal closures
  • Continued fraction algorithm for rational approximation

See Also

Source

Header file: `src/CglGMI/CglGMI.hpp`