"Nonsmooth dynamics associated to variational inequalities, generalized Nash games and applications"

“与变分不等式相关的非光滑动力学、广义纳什博弈和应用”

• 批准号: 262899-2012
• 负责人: Cojocaru, MonicaGabriela
• 金额: $ 1.09万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=548062
• 关键词: Nonsmooth; dynamics; associated; variational; inequalities

This proposal investigates the relationship between three important mathematical constructs: nonsmooth dynamical systems, quasivariational inequalities, and generalized Nash games, and their appropriate applications. Variational inequalities (VI) were introduced in the early 60s within the framework of partial differential equations. Later it was shown they equivalently reformulate large classes of equilibrium problems (such as Nash, Wardrop, Walras, Cournot, traffic equilibrium etc.), thus becoming prominent in operations research. Due to this equivalence, solutions of VI are often called equilibria. Of specific interest in my work is a particular class of VI, called "quasivariational" (QVI). Essentially a QVI models equilibrium problems with constraint sets dependent on the equilibrium solution.

该提案调查了三个重要的数学结构之间的关系：非平滑动力学系统，准偏差不平等，广义的NASH游戏及其适当的应用。在偏微分方程的框架内，在60年代初引入了变异不平等（VI）。后来，人们表明他们等效地重新制定了大量的均衡问题（例如纳什，沃德罗普，沃尔拉斯，库诺特，交通平衡等），从而在运营研究中变得突出。由于这种等效性，VI的溶液通常称为平衡。我的工作中特别感兴趣的是一类VI类，称为“ Quasivariational”（QVI）。本质上，QVI模型的平衡问题与限制集取决于平衡解决方案。