MCAA: Applied Matrix-free Constrained Nonlinear Programming Problems and Algorithms to Approximate their Solution

MCAA：应用无矩阵约束非线性规划问题和算法来逼近其解决方案

• 批准号: 9977986
• 负责人: Anthony Kearsley
• 金额: $ 6万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9977986&HistoricalAwards=false
• 关键词: MCAA; Applied; Matrix; free; Constrained

This proposal outlines a program to develop a class of matrix-free algorithms for the solution of nonlinearlyconstrained optimization problems. Of special interest are problems arising in modeling and simulation ofindustrially important materials. Numerical algorithms will be developed, implemented and tested, and thenreleased as public domain software. These matrix-free algorithms will, in turn, be employed as educational tools. In particular, when teaching numerical methods (like Finite Element or Finite Difference Methods) in undergraduate classes, these methods will be used to shift the emphasis away from linear-algebraic issues (like building mass and stiffness matrices) allowing a stronger emphasis to be placed on methodology. The linear-algebraic details can then be left for more advanced classes.

本文提出了一种无矩阵算法的方案，用于求解非线性约束优化问题。特别感兴趣的是在工业上重要的材料的建模和模拟中出现的问题。数值算法将被开发、实现和测试，然后作为公共领域软件发布。 这些无矩阵算法将反过来被用作教育工具。特别是，在本科课程中教授数值方法（如有限元或有限差分法）时，这些方法将用于将重点从线性代数问题（如建筑质量和刚度矩阵）转移，从而更加强调方法论。线性代数的细节可以留给更高级的课程。