Discrete Choice Prox-Functions on the Simplex

David Müller (), Yurii Nesterov () and Vladimir Shikhman ()
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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

Mathematics of Operations Research, 2022, vol. 47, issue 1, 485-507

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.

Keywords: Primary: 90C25; secondary: 90C90; convex programming; prox-function; discrete choice; additive random utility models; dual averaging; consumption cycle (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:485-507

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