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摘要翻译：
在离散选择模型下的经典优化问题中，决策者控制每个产品的一个属性。通常，该属性是产品的价格。然而，价格并不是影响产品市场占有率和利润率的唯一因素。本文将经典的价格优化问题推广到允许对每个产品的选择控制多个属性。以往的研究表明，经典的价格优化问题可以在多种选择模型下有效地求解，如市场份额重构等方法。然而，这些方法不能应用于广义问题。我们证明了广义问题在多项式logit(MNL)、嵌套logit(NL)和马尔可夫链(MC)选择模型下仍然是可处理的。这类问题仍然可以转化为凸规划，在一定的假设条件下存在最优解。我们还证明了市场份额中的线性约束（如资源约束）可以加入到优化问题中，并且可处理性结果仍然成立。
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英文标题：
《Tractable Constrained Optimization over Multiple Product Attributes
under Discrete Choice Models》
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作者：
Hongzhang Shao, Anton J. Kleywegt
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最新提交年份：
2020
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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：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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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：
In classical optimization problems under discrete choice models, the decision maker control one attribute of each product. Usually, that attribute is the product's price. However, price is not the only attribute that can impact both the product's market share and profit margin. In this paper, we generalize the classical price optimization problem to allow multiple attributes to be controlled over each choice of product. Past research showed that the classical price optimization problem can be solved efficiently under many choice models, using methods such as the market share reformulation. However, these methods cannot be applied to the generalized problem. We show that the generalized problem is still tractable under the multinomial logit (MNL), the nested logit (NL) and the Markov chain (MC) choice model. Such problems can still be transformed into convex programs, and optimal solutions exist under certain assumptions. We also show that linear constraints in market shares (e.g. resource constraints) can be added to the optimization problems, and the tractability results still hold.
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PDF链接：
https://arxiv.org/pdf/2007.09193
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