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Regularized Mathematical Programs with Stochastic Equilibrium Constraints: Estimating Structural Demand Models.

机译：具有随机均衡约束的规则化数学程序：估计结构需求模型。

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The article considers a particular class of optimization problems involving set-valued stochastic equilibrium constraints. A solution procedure is developed by relying on an approximation scheme for the equilibrium constraints, based on regularization, that replaces them by equilibrium constraints involving only single-valued Lipschitz continuous functions. In addition, sampling has the further effect of replacing the simplified equilibrium constraints by more manageable ones obtained by implicitly discretizing the (given) probability measure so as to render the problem computationally tractable. Convergence is obtained by relying, in particular, on the graphical convergence of the approximated equilibrium constraints. The problem of estimating the characteristics of a demand model, a widely studied problem in micro-economics, serves both as motivation and illustration of the regularization and sampling procedure.

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Chen, X.; Sun, H.; Wets, R. J.;
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年度 2013
页码 1-25
总页数 25
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Mathematical programming; Approximation(Mathematics); Convergence; Equilibrium(General); Stochastic processes; Graphical convergence; Monotone linear complementarity problem; Regularization; Sample average approximation; Stochastic equilibrium;

机译：数学规划;逼近（数学）;收敛;均衡（一般）;随机过程;图形收敛;单调线性互补问题;正则化;样本平均逼近;随机均衡;

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专利

1. REGULARIZED MATHEMATICAL PROGRAMS WITH STOCHASTIC EQUILIBRIUM CONSTRAINTS: ESTIMATING STRUCTURAL DEMAND MODELS [J] . Chen Xiaojun, Sun Hailin, Wets Roger J. -B. SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics . 2015,第1期

机译：带有随机平衡约束的正则化数学程序：估计结构需求模型
2. An entropic regularization approach for mathematical programs with equilibrium constraints [J] . S. Ilker Birbil, Shu-Cherng Fang, Jiye Han Computers & operations research . 2004,第13期

机译：具有平衡约束的数学程序的熵正则化方法
3. Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization [J] . Gui-Hua Lin, Xiaojun Chen, Masao Fukushima Mathematical Programming . 2009,第1a2期

机译：通过逼近求解具有平衡约束的随机数学程序，并通过惩罚平滑隐式程序
4. A Brief Overview of Stochastic Equilibrium Problems and Stochastic Mathematical Programs with Equilibrium Constraints [C] . Gui-Hua Lin, Masao Fukushima The 8th international conference on optimization: Techniques and Applications . 2010

机译：带有平衡约束的随机平衡问题和随机数学程序的简要概述
5. Mathematical programs with equilibrium constraints (MPECs) in process systems engineering. [D] . Baumrucker, Brian T. 2009

机译：过程系统工程中具有平衡约束（MPEC）的数学程序。
6. Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models. [O] . I P Tomlinson, W F Bodmer 1995

机译：程序性细胞死亡和分化失败是肿瘤的原因：一些简单的数学模型。
7. Regularized mathematical programs with stochastic equilibrium constraints : estimating structural demand models [O] . Chen X, Sun H, Wets RJB 2015

机译：具有随机均衡约束的正则化数学程序：估计结构需求模型

Regularized Mathematical Programs with Stochastic Equilibrium Constraints: Estimating Structural Demand Models.

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