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# 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} }

- Published 2007 in SODA

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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