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Discrete Choice Prox-Functions on the Simplex

Author

Listed:
  • David Müller

    (Department of Mathematics, Chemnitz University of Technology, 09126 Chemnitz, Germany)

  • Yurii Nesterov

    (Center for Operations Research and Econometrics, Catholic University of Louvain, 1348 Louvain-la-Neuve, Belgium)

  • Vladimir Shikhman

    (Department of Mathematics, Chemnitz University of Technology, 09126 Chemnitz, Germany)

Abstract

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.

Suggested Citation

  • David Müller & Yurii Nesterov & Vladimir Shikhman, 2022. "Discrete Choice Prox-Functions on the Simplex," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 485-507, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:485-507
    DOI: 10.1287/moor.2021.1136
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