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

用于解决变分不等式、互补性和非线性规划问题的鲁棒全局非平滑牛顿法

• 批准号: 9104078
• 负责人: Jong-Shi Pang
• 金额: $ 15.01万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-15 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104078&HistoricalAwards=false
• 关键词: Robust; Global; Nonsmooth; Newton; Methods

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.

本项目致力于开发、分析和实现一种稳健的、全局收敛的、基于非光滑方程的逐次二次规划(NE/SQP)方法，用于求解有限维变分不等式、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，其基础是将这三类重要的数学规划共同重新表述为一个非光滑方程组，其中应用了光滑方程组的经典高斯-牛顿法的扩展/修改。一些初步的收敛结果和以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均衡问题以及科学和工程中各种不同学科的优化问题的主要实用工具。