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Convexification of Permutation-Invariant Sets

Author

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  • Jinhak Kim
  • Mohit Tawarmalani
  • Jean-Philippe P. Richard

Abstract

In this paper, we characterize the convex hull of a set, which does not change when variables are permuted, as a projection of a set in a higher-dimensional space. In particular, we show that as long as the set can be convexified after imposing an ordering on the constituent variables, the convex hull of the set can be written using a polynomial number of additional variables and constraints.

Suggested Citation

  • Jinhak Kim & Mohit Tawarmalani & Jean-Philippe P. Richard, 2019. "Convexification of Permutation-Invariant Sets," Purdue University Economics Working Papers 1315, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1315
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    File URL: https://business.purdue.edu/research/working-papers-series/2019/1315.pdf
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    References listed on IDEAS

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    1. Anonymous, 2011. "Notes from the Editors," American Political Science Review, Cambridge University Press, vol. 105(4), pages 1-1, November.
    2. Anonymous, 2011. "Notes from the Editors," American Political Science Review, Cambridge University Press, vol. 105(1), pages 1-1, February.
    3. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    4. J. N. R. Jeffers, 1967. "Two Case Studies in the Application of Principal Component Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 16(3), pages 225-236, November.
    5. Anonymous, 2011. "Notes from the Editors," American Political Science Review, Cambridge University Press, vol. 105(3), pages 1-1, August.
    6. Anonymous, 2011. "Notes from the Editors," American Political Science Review, Cambridge University Press, vol. 105(2), pages 1-1, May.
    7. Egon Balas, 2004. "Logical Constraints as Cardinality Rules: Tight Representation," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 115-128, June.
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