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

本课题主要研究基于非光滑方程组的最优化问题和变分不等式的理论和计算。在理论方面，目标是通过发展一个全面的理论，通过非光滑方程的近似，更好地理解这些数学程序的敏感性、稳定性和其他内在性质。在计算方面，目标是依赖于光滑方程的经典牛顿方法在非光滑背景下的推广，开发出求解这些数学规划的稳健的、全局的、局部二次收敛的算法。这项研究是建立在最近几年的工作基础上的，这些工作证明了这种非光滑方程方法对于变分不等式、互补问题和非线性规划的丰硕成果。

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.