# Complexity of cutting planes and branch-and-bound in mixed-integer optimization

@article{Basu2020ComplexityOC, title={Complexity of cutting planes and branch-and-bound in mixed-integer optimization}, author={Amitabh Basu and Michele Conforti and Marco Di Summa and Hongyi Jiang}, journal={ArXiv}, year={2020}, volume={abs/2003.05023} }

We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP does at least as well as BB, with variable disjunctions. We sharpen this by giving instances of the stable set problem where we can provably establish… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 73 REFERENCES

## An Exponential Lower Bound on the Length of Some Classes of Branch-and-Cut Proofs

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Chvátal closures for mixed integer programming problems

VIEW 1 EXCERPT

## Gomory cuts revisited

VIEW 1 EXCERPT

## Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL