经济生活中的逆变分不等式 --- 应用与算法
首发时间:2006-09-18
摘要: 变分不等式中自变量与映射互换位置的数学问题称为逆变分不等式. 本文以现实生活中的一些问题为例, 详细说明逆变分不等式(与变分不等式一样)广泛出现在交通控制、经济平衡和管理科学的许多领域. 文章同时研究了逆变分不等式的一些性质并介绍了求解单调逆变分不等式的一些方法. 现实生活中的变分不等式和逆变分不等式, 其函数一般没有显式表达式, 只能对给定的自变量, 观测到相应的函数值, 并且这种观测往往是代价不菲的. 因此提供求解变分不等式及逆变分不等式的只用函数值且尽可能少用函数值的方法, 是解决一大批实际问题的需要, 是值得进一步研究的课题.
关键词: 变分不等式, 逆变分不等式, 单调性
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Inverse Variational Inequalities in Economics ---- Applications and Algorithms
Abstract: We call the mathematical form of such problems an inverse variational inequality (IVI), if the variable and the function are in the opposite positions of the classical variational inequality (VI). IVIs arise from many real-life areas such as economics, transportation, management science and etc. This paper studies some properties of IVIs and introduces some algorithms for solving monotone IVIs. For the problems arising from the real world, usually the functions do not have any explicit forms. Only for given variable, the function value can be obtained via costly observations. Establishing efficient numerical methods for solving VIs and IVIs which only use function values is necessary for practical problems and thus is still a worthful investigation project.
Keywords: Variational inequalities, inverse variational inequalities, monotonicity
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