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Discrete choice prox-functions on the simplex

Author

Listed:
  • Müller, David

    (Chemnitz University of Technology)

  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Shikhman, Vladimir

    (Chemnitz University of Technology)

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 natural 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 naturally adjusts demand within a consumption cycle.

Suggested Citation

  • Müller, David & Nesterov, Yurii & Shikhman, Vladimir, 2023. "Discrete choice prox-functions on the simplex," LIDAM Reprints CORE 3242, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3242
    DOI: https://doi.org/10.1287/moor.2021.1136
    Note: In: Mathematics of Operations Research, 2022, vol. 47(1), p. 485-507
    as

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