Nonsmooth Equations Approach to Optimization and Variational Inequality: Theory and Computation

本计画将探讨最佳化问题与变分不等式的理论与计算，并将其等价公式化为 非光滑方程 在理论方面，目标是通过发展一个全面的理论 非光滑方程通过他们的近似，更好地理解灵敏度，稳定性，和其他的数学程序的内在属性。 在计算方面，我们的目标是发展，依靠推广的经典牛顿方法光滑方程的非光滑背景下，一些强大的，全球性的， 局部二次收敛算法来解决这些数学规划。 这项研究是建立在近年来的工作已经证明了这种非光滑方程的方法，变分不等式，互补问题和非线性规划的成果。

This project investigates the theory and computation of optimization problems and variational inequalities based on their equivalent formulation as a of nonsmooth equations. On the theoretical side, the goal is to gain, through the development of a comprehensive theory nonsmooth equations via their approximations, a better understanding of the sensitivity, stability, and other instrinsic properties of these mathematical programs. On the computational side, the goal is to develop, relying on generalizations of the classical Newton methods for smooth equations to the nonsmooth context, some robust, globally, locally quadratically convergent algorithms for solving these mathematical programs. The research is built on work in recent years which has demonstrated the fruitfulness of this nonsmooth-equations approach to variational inequalities, complementarity problems, and nonlinear programs.