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

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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.