Robust, Global Nonsmooth Newton Methods for Variational Inequality, Complementarity and Nonlinear Programming Problems

本项目关注的是一种鲁棒的、全局收敛的、基于非光滑方程的连续二次规划（NE/SQP）方法的开发、分析和实现，该方法用于解决有限维变分不等式、非线性互补和非线性规划问题。该方法是一种迭代下降算法，该算法基于将这三种重要的数学程序作为非光滑方程系统的共同重新表述，并对光滑方程的经典高斯-牛顿方法进行了扩展/修改。一些初步的收敛结果已经建立，并且先前的全局非光滑牛顿方法的计算经验表明，新的和改进的NE/SQP方法可以成为解决各种系统工程和经济平衡问题的主要实用工具。也适用于科学和工程中不同学科产生的各种优化问题。

This project is concerned with the development, analysis and implementation of a robust, globally convergent, Nonsmooth Equation Based, Successive Quadratic Programming (NE/SQP) method for solving the finite-dimensional variational inequality, nonlinear complementarily and nonlinear programming problems. The method is an iterative descent algorithm that is based on a common reformulation of these three important classes of mathematical programs as a system of nonsmooth equations, to which an extension/modification of the classical Gauss-Newton method for smooth equations is applied. Some preliminary convergence results have been established, and computational experience with previous global non-smooth Newton methods suggests that the new and improved NE/SQP method could become a major practical tool for solving various kinds of systems engineering and economics equilibrium problems, as well as for a variety of optimization problems arising from diverse disciplines in science and engineering.