Workshop on Numerical Linear Algebra and Optimization

该基金为参加为期三天的“数值线性代数与优化研讨会”的美国科学家提供旅费支持，该研讨会将于2013年8月8日至10日在加拿大温哥华的不列颠哥伦比亚大学举行。研讨会有以下三个目标：(1)将线性代数和优化学界聚集在一起，以促进互动，探索这两个研究领域交叉的丰富领域；(2)寻求这些问题在机器学习和控制等领域的应用；(3)推动和讨论在科学和工业优化中积极使用大规模数值线性代数工具的问题。研讨会将重点讨论的一个主要领域是特征值优化，这是近年来备受关注的问题，两个社区从不同的角度对其进行了研究。优化是一个很大的研究领域，其应用范围从经济学和工程学到国家安全、能源和气候理解。可以在优化的帮助下解决的问题包括在原材料限制下制造各种商品时利润最大化或浪费最小化；基于计算机的物体分类学习（例如，区分坦克和树木）；设计受体积和环境限制的更坚固的建筑物；通过避免某些不受欢迎的振动频率，使飞机更安全。此类优化问题的解决方案需要使用线性代数量（如特征值），并且必须以最有效的方式谨慎地进行此类量的大量计算。这是数值线性代数的中心任务，其工具已被各种优化社区采用和调整以适应他们的需要。在优化和数值线性代数这两个领域之间有一个非常丰富的研究领域，本次研讨会的组织者旨在看到两个社区共同努力解决工业中出现的重要问题。

This grant provides travel support for US scientists to a three-day "Workshop on Numerical Linear Algebra and Optimization", to be held August 8-10, 2013 at the University of British Columbia, Vancouver, Canada. The workshop has the following three objectives: (1) to bring together the community of linear algebra and optimization in order to foster interaction and explore the rich area at the intersection of these two research fields; (2) to seek application of these problems in fields like machine learning and control; and (3) to promote and discuss the issue of actively using large-scale numerical linear algebra tools in scientific and industrial optimization. One of the main areas the workshop will focus on is eigenvalue optimization, which has received a lot of attention recently and which is studied by the two communities from different perspectives.Optimization is a large field of research, with applications ranging from economics and engineering to national security, energy, and climate understanding. Examples of problems that can be solved with the help of optimization include maximizing profit or minimizing waste when manufacturing a variety of goods under raw material constraints; computer-based learning to classify objects (e.g., distinguishing tanks from trees); designing stronger buildings subject to volume and environmental constraints; and making planes safer by avoiding certain undesirable vibration frequencies. Solutions to such optimization problems need to make use of linear algebra quantities (like eigenvalues), and extensive calculations of such quantities must be done with care and in the most efficient way. This is a central task in numerical linear algebra, the tools of which have been adopted and adapted by various optimization communities to suit their needs. There is a very rich area of research at the interface between these two fields of optimization and numerical linear algebra, and the organizers of this workshop aim to see both communities work together toward addressing the important problems that arise in industry.