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

这一建议研究了三个重要的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Nash对策，以及它们的适当应用。变分不等式(VI)是在60年代初在偏微分方程组的框架内引入的。后来的研究表明，它们等价地重新表述了一大类均衡问题(如纳什、瓦洛普、沃尔拉斯、古诺、交通均衡等)，从而在运筹学中变得突出起来。由于这种等价性，VI的解通常被称为平衡。在我的工作中，我特别感兴趣的是一类特殊的VI，称为“准变分”(QVI)。本质上，QVI模拟均衡问题，约束集依赖于均衡解。

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.