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

这项建议概述了一个计划，以开发一类无矩阵的算法来解决非线性约束优化问题。特别令人感兴趣的是在对极其重要的材料进行建模和模拟时出现的问题。数值算法将被开发、实施和测试，然后作为公共领域软件发布。这些与矩阵无关的算法将被用作教育工具。特别是，当在本科课堂上教授数值方法(如有限元或有限差分法)时，这些方法将被用于将重点从线性代数问题(如建立质量和刚度矩阵)转移到允许更强调方法论的地方。线性代数的细节可以留给更高级的课程。

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.