"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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=594778
• 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.

该提案研究了三个重要数学结构之间的关系：非光滑动力系统、拟变分不等式和广义纳什博弈及其适当的应用。变分不等式 (VI) 于 20 世纪 60 年代初在偏微分方程的框架内引入。后来的研究表明，他们等效地重新表述了大类均衡问题（例如纳什、沃德罗普、瓦尔拉斯、古诺、交通均衡等），从而在运筹学中变得突出。由于这种等价性，VI 的解通常称为均衡。我的工作中特别感兴趣的是一类特殊的 VI，称为“准变分”(QVI)。本质上，QVI 对平衡问题进行建模，其约束集取决于平衡解。