U.S.-France (INRIA) Cooperative Research: Numerical Methodsfor Nonlinear Optimization

该奖项将支持西北大学的Jorge Nocedal博士和法国国家信息科学与自动化研究所（INRIA）的Claude LeMarechal博士在计算机科学方面的持续合作研究。该项目的主要目标是求解大规模非线性优化问题。变分同化技术是天气预报中最有前途的方法之一，它可以用来调整各种物理量，包括强迫数据。它的多功能性是由于这个问题的物理性质同时包含在成本函数和约束条件中。基本问题是数值模型初始条件的确定。由于观测值非常稀疏，关键思想是利用非线性优化代码估计未知观测值。一旦确定了一组良好的初始条件，就可以通过模拟动力学问题来进行大气和海洋预报。在这个项目中，dr。Nocedal和LeMarechal计划制定一个试点代码，其中包括将在气象学同化问题上进行测试的算法和理论发展。这个项目将会发展并纳入新的算法思想，并将在未来应用于另外两个领域：晶体学和跨音速流。该项目将受益于两位研究人员在拟议研究主题方面的互补专业知识。

This award will support continued collaborative research in computer science between Dr. Jorge Nocedal, Northwestern University, and Dr. Claude LeMarechal, French National Institute for Information Science and Automation (INRIA). The main object of the project is the solution of large scale non-linear optimization problems. One of the most promising approaches in weather forecasting is the variational assimilation technique, which can be used to adjust various physical quantities, including the forcing data. Its versatility is due to the fact that the physics of the problem is incorporated both in the cost function and in the constraints. The fundamental problem is the determi- nation of initial conditions for the numerical models. Since observations are very sparse, the key idea is to estimate the unknown observations by means of the nonlinear optimization code. Once a good set of initial conditions has been determined, atmospheric and oceanographic forecasting can be performed by simulation of the dynamical questions. In this project, Drs. Nocedal and LeMarechal plan to develop a pilot code, encompassing algorithmic and theoretical developments that will be tested on the assimilation problem in meteorology. This program will evolve to incorporate new algorithmic ideas and will also be applied in the future to two other areas: crystallography and transonic flow. This project will benefit from complementary expertise of the two investigators in the proposed topic of research.