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有限理性下参数最优化问题解的稳定性

杨光惠1  杨辉1,*  向淑文1   

  1. 1. 贵州大学数学与统计学院, 贵阳 550025
  • 收稿日期:2015-08-31 出版日期:2016-12-15 发布日期:2016-12-15
  • 通讯作者: 杨辉 hui-yang@163.com
  • 基金资助:

    国家自然科学基金(Nos. 11271098, 11161008), 贵州省科学技术基金(No. 20132116), 贵州大学青年教师基金(No. 2012002)

 Stability of solutions to parametric optimization problems under bounded rationality

YANG Guanghui1  YANG Hui1,*   XIANG Shuwen1   

  1. 1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
  • Received:2015-08-31 Online:2016-12-15 Published:2016-12-15

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542

被引次数

1

摘要：

主要研究有限理性下参数最优化问题解的稳定性. 即在两类扰动即目标函数及可行集二者, 目标函数、可行集及参数三者分别同时发生扰动的情形下, 对参数最优化问题引入一个抽象的理性函数, 分别建立了参数最优化问题的有限理性模型M, 运用``通有''的方法, 得到了上述两种扰动情形下相应的有限理性模型M的结构稳定性及对\varepsilon-平衡(解)的鲁棒性, 即有限理性下绝大多数的参数最优化问题的解都 是稳定的, 并以一个例子说明所得的稳定性结果均是正确的.

关键词: 参数最优化, 有限理性, 稳定性

Abstract:

 Parametric optimization has been widely applied in game theory, control theory, economics and management, engineering technology, etc. Recently, the stability of solutions to parametric optimization has attracted increasing attention. This paper mainly studies the stability of solutions to parametric optimization problems under bounded rationality. By introducing an abstract rationality function, two rational models M are established with two types of perturbations: the perturbation of both objective functions and feasible sets, and the perturbation of objective functions, feasible sets and parameters simultaneously. For the two perturbations above, by the ``generic'' method, the rational model M is structurally stable and is robust to \varepsilon-equilibria (or solutions), respectively. That is, the solutions to most of parametric optimization problems are stable in the sense of Baire category. Finally, an example is illustrated.

Key words: parametric optimization, bounded rationality, stability