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Lifted polymatroid inequalities for mean-risk optimization with indicator variables

Author

Listed:
  • Alper Atamtürk

    (University of California)

  • Hyemin Jeon

    (University of California)

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.

Suggested Citation

  • Alper Atamtürk & Hyemin Jeon, 2019. "Lifted polymatroid inequalities for mean-risk optimization with indicator variables," Journal of Global Optimization, Springer, vol. 73(4), pages 677-699, April.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:4:d:10.1007_s10898-018-00736-z
    DOI: 10.1007/s10898-018-00736-z
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    References listed on IDEAS

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    Cited by:

    1. Alper Atamtürk & Carlos Deck & Hyemin Jeon, 2020. "Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 346-355, April.
    2. Andrés Gómez & Oleg A. Prokopyev, 2021. "A Mixed-Integer Fractional Optimization Approach to Best Subset Selection," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 551-565, May.

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