Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lovász extension and non-smooth convex optimization

@inproceedings{Chudak2007EfficientST,
  title={Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lov{\'a}sz extension and non-smooth convex optimization},
  author={Fabi{\'a}n A. Chudak and Kiyohito Nagano},
  booktitle={SODA},
  year={2007}
}
We consider convex relaxations for combinatorial optimization problems with submodular penalties. The relaxations are obtained very naturally through a novel use of the Lovász extension of a submodular function. We also propose the use of simple and recent algorithms for non-smooth convex optimization due to Nesterov to approximately solve them. For the uncapacitated facility location problem with submodular penalties we design FPTAS for our relaxation that can be used to design approximation… CONTINUE READING

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References

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Showing 1-8 of 8 references

Submodular functions and convexity. Mathematical Programming — The State of the Art

  • L. Lovász
  • eds. , Springer-Verlag,
  • 1983
Highly Influential
4 Excerpts

Zuiki: A network flow approach to cost allocation for rooted

  • N. S. Iwata
  • trees. Networks,
  • 2004
Highly Influential
3 Excerpts

Hong: About strongly polynomial time algorithm for quadratic optimization over submodular constraints

  • D. S. Hochbaum, S.-P
  • Mathematical Programming,
  • 1995
Highly Influential
3 Excerpts

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