Lifted polymatroid inequalities for mean-risk optimization with indicator variables

  • Alper AtamtürkEmail author
  • Hyemin Jeon


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.


Risk Submodularity Polymatroid Conic integer optimization Valid inequalities 



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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Authors and Affiliations

  1. 1.Industrial Engineering and Operations ResearchUniversity of CaliforniaBerkeleyUSA

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