Outer-product-free sets for polynomial optimization and oracle-based cuts

@article{Bienstock2016OuterproductfreeSF,
  title={Outer-product-free sets for polynomial optimization and oracle-based cuts},
  author={Daniel Bienstock and Chen Chen and Gonzalo Mu{\~n}oz},
  journal={Mathematical Programming},
  year={2016},
  pages={1-44}
}
  • Daniel Bienstock, Chen Chen, Gonzalo Muñoz
  • Published 2016
  • Mathematics
  • Mathematical Programming
  • This paper introduces cutting planes that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $$S\cap P$$ S ∩ P , where S is a closed set, and P is a polyhedron. Given an oracle that provides the distance from a point to S , we construct a pure cutting plane algorithm which is shown to converge if the initial relaxation is a polyhedron. These cuts are generated from convex… CONTINUE READING

    Figures and Tables from this paper.

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 15 CITATIONS

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 109 REFERENCES

    Intersection Cuts - A New Type of Cutting Planes for Integer Programming

    VIEW 2 EXCERPTS

    Generalized intersection cuts and a new cut generating paradigm

    VIEW 2 EXCERPTS
    HIGHLY INFLUENTIAL

    On the complexity of four polyhedral set containment problems

    VIEW 6 EXCERPTS
    HIGHLY INFLUENTIAL

    On Minimal Valid Inequalities for Mixed Integer Conic Programs

    VIEW 3 EXCERPTS

    Optimizing over the split closure

    VIEW 1 EXCERPT

    Optimizing a polyhedral-semidefinite relaxation of completely positive programs

    • Samuel Burer
    • Mathematics, Computer Science
    • Math. Program. Comput.
    • 2010
    VIEW 1 EXCERPT