Gomory cuts in integer programming
E718425
Gomory cuts in integer programming are a class of cutting-plane techniques that iteratively refine linear programming relaxations to find optimal integer solutions to mixed-integer optimization problems.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Gomory cuts | 0 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
cutting-plane method
ⓘ
integer programming technique ⓘ optimization method ⓘ |
| appliedAt | nodes of a branch-and-bound tree ⓘ |
| appliesTo |
mixed-integer linear programming
ⓘ
pure integer linear programming ⓘ |
| assumption | variables have integrality restrictions ⓘ |
| basedOn | linear programming relaxation ⓘ |
| belongsTo | polyhedral theory of integer programming ⓘ |
| canBe | generated automatically by MIP solvers ⓘ |
| category | exact algorithmic technique ⓘ |
| characteristic |
derived from simplex tableau rows
ⓘ
separate current fractional solution ⓘ valid inequalities for integer hull ⓘ |
| developedBy | Ralph E. Gomory NERFINISHED ⓘ |
| effect | tightens feasible region toward integer hull ⓘ |
| field |
integer programming
ⓘ
mathematical optimization ⓘ operations research ⓘ |
| goal |
eliminate fractional solutions
ⓘ
enforce integrality of variables ⓘ tighten LP relaxation ⓘ |
| hasVariant |
Gomory fractional cut
NERFINISHED
ⓘ
Gomory mixed-integer cut NERFINISHED ⓘ pure-integer Gomory cut NERFINISHED ⓘ |
| implementedIn |
commercial MILP solvers
ⓘ
open-source MILP solvers ⓘ |
| improves |
lower bound for maximization problems
ⓘ
upper bound for minimization problems ⓘ |
| influenced | development of modern cutting-plane methods ⓘ |
| introducedIn | 1950s ⓘ |
| methodType |
cutting-plane algorithm
ⓘ
iterative refinement method ⓘ |
| namedAfter | Ralph E. Gomory NERFINISHED ⓘ |
| property |
can be applied iteratively until integrality is reached
ⓘ
do not remove any feasible integer solution ⓘ remove at least the current fractional LP solution ⓘ |
| relatedTo |
Chvátal–Gomory cuts
NERFINISHED
ⓘ
branch-and-cut NERFINISHED ⓘ simplex method ⓘ |
| requires | fractional basic variable in tableau ⓘ |
| typicalInput | optimal basis of LP relaxation ⓘ |
| typicalOutput | linear inequality added to LP ⓘ |
| usedFor |
finding optimal integer solutions
ⓘ
improving bounds in branch-and-bound ⓘ solving mixed-integer optimization problems ⓘ |
Referenced by (1)
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