Discrete choice prox-functions on the simplex

David Müller, Yurii Nesterov () and Vladimir Shikhman
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David Müller: Chemnitz University of Technology
Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium
Vladimir Shikhman: Chemnitz University of Technology

No 3242, LIDAM Reprints CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Convex programming; prox-function; discrete choice; additive random utility models; dual averaging; consumption cycle (search for similar items in EconPapers)
Pages: 28
Date: 2023-01-01
Note: In: Mathematics of Operations Research, 2022, vol. 47(1), p. 485-507
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvrp:3242

DOI: 10.1287/moor.2021.1136

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