摘要翻译：
从离散选择的可加随机效用模型出发，导出了单纯形上新的Prox函数。它们是相应剩馀函数的凸共轭。特别地，我们显式地导出了与广义极值模型，特别是与广义嵌套logit模型相关的离散选择函数的凸性参数。结合到次梯度格式中，离散选择Prox函数导致迭代步骤的自然概率解释。作为例证，我们讨论了离散选择函数在消费者理论中的一个经济应用。凸规划的对偶平均方案自然地调整消费周期内的需求。
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英文标题：
《Discrete choice prox-functions on the simplex》
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作者：
David M\"uller and Yurii Nesterov and Vladimir Shikhman
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1909.05591