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
- CglGMIParam for parameter settings
- CglGomory for simpler Gomory implementation
Source
Header file: `src/CglGMI/CglGMI.hpp`