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Lifted polymatroid inequalities for mean-risk optimization with indicator variables

  • Alper AtamtürkEmail author
  • Hyemin Jeon
Article
  • 19 Downloads

Abstract

We investigate a mixed 0–1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities by lifting the polymatroid inequalities on the binary variables. Computational experiments demonstrate the effectiveness of the inequalities in strengthening the convex relaxations and, thereby, improving the solution times for mean-risk problems with fixed charges and cardinality constraints significantly.

Keywords

Risk Submodularity Polymatroid Conic integer optimization Valid inequalities 

Notes

Acknowledgements

This research is supported, in part, by Grant FA9550-10-1-0168 from the Office of the Assistant Secretary of Defense for Research and Engineering.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeleyUSA

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