CAREER: Research in Nonlinear Numerical Optimization and Practicums for Computational Science

由于分析原因，许多科学和工程数值优化问题在计算上既昂贵又难以解决。毫不奇怪，对于这些问题，在描述系统被优化的软件的集成方面也存在重大问题。这些困难往往是交织在一起的。将要完成的研究将着眼于在解决这些困难的数值优化问题时出现的分析和算法问题。具体来说，这项工作将沿着两条互补的路线发展：非线性优化的模式搜索方法的进一步发展和分析，以及使用近似模型优化由计算昂贵函数定义的系统的技术的设计和分析。这两条研究路线都包括在软件开发和实验方面的大量工作。从科学和工程中处理数值优化问题的实践经验揭示了当前计算机科学课程中没有很好地涵盖的问题和技术，但这些问题和技术可以很好地服务于任何多学科计算设置的学生。课程开发将利用计算机科学和计算数学中的现有知识和软件工具来设计新的课程——实际上是实习——这将教会学生更多关于如何理解、维护、增强和优化现有科学软件的知识。重点将放在着眼于性能编程的系统分析和测试上。这种方法的基础是相信学生应该被教导如何以系统的、科学的方式进行实验，以分析和推理现存的、复杂的计算机程序。

Many scientific and engineering numerical optimization problems are both computationally expensive and difficult to solve for analytical reasons. Not surprisingly, for such problems there are also significant issues in the integration of the software that describes the system being optimized. These difficulties are often intertwined. The research that will be done will look at analytical and algorithmic issues that arise in the solution of such difficult numerical optimization problems. Specifically, the work will evolve along two complementary lines: the further development and analysis of pattern search methods for nonlinear optimization, and the design and analysis of techniques for using approximation models to optimize systems defined by computationally expensive functions. Both these lines of research include a strong effort in software development and experimentation. Practical experience working on numerical optimization problems from science and engineering reveals issues and techniques that are not covered well in the current computer science curriculum and yet would serve students well in any multidisciplinary computational setting. The course development will draw upon existing knowledge and software tools in computer science and computational mathematics to design new courses---practicums, in effect---that will teach students more about how to understand, maintain, enhance, and optimize existing scientific software. The emphasis will be on systematic analysis and testing with an eye toward performance programming. Fundamental to this approach is the belief that students should be taught how to experiment in a systematic, scientific fashion to analyze and reason about extant, complex computer programs.