计算捆绑定价问题选择概率的梯度下降算法  

A gradient descent algorithm for computing choice probability in the bundle size pricing problem

作　　者：张立平[1] 赵逸潭 Liping Zhang;Yitan Zhao

机构地区：[1]清华大学数学科学系,北京100084

出　　处：《中国科学:数学》2025年第2期385-396,共12页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:12171271)资助项目。

摘　　要：捆绑定价问题在服务业、电视和电影、媒体等行业有重要的应用,得到了广泛研究.本文证明捆绑定价问题交叉矩模型的目标函数在约束域内是强凸的且梯度是Lipschitz连续的.基于此性质,本文提出求解该模型的梯度下降算法并计算捆绑定价问题选择概率.本文还证明了算法是线性收敛的.数值实验验证了算法的有效性和交叉矩模型对于选择概率估计的准确性.Bundle size pricing has important applications in the service industry,TV and film,media,and other industries and so has been widely studied.In this paper,we prove that the objective function of the cross-moment model of the bundle size pricing problem is strongly convex and the gradient is Lipschitz continuous in the constrained region.Based on this property,we propose a gradient descent algorithm to compute choice probability by solving this model.Moreover,we prove that the proposed algorithm is linearly convergent.Numerical experiments verify the effectiveness of the algorithm and the accuracy of the cross-moment model for the choice probability estimation.

关 键 词：捆绑定价 交叉矩模型 梯度下降算法 选择概率 

分 类 号：F274[经济管理—企业管理] O224[经济管理—国民经济]