The purpose of this project is to develop numerical methods for solving large scale unconstrained optimization problems. Special attention will be given to strategies for dynamically scaling the variables, and to the study of the structure of problems arising in areas such as transonic flow, neuron networks and meteorology. New preconditioners will be developed to be used in conjunction with the discrete truncated Newton method, and the performance of this method will be compared with that of limited memory and partitioned quasi.Newton methods. The project will also investigate decomposition principles which allow solving a large nonlinear problem as a sequence of simpler problems. limited memory BFGS code for solving very large nonlinear problems will be developed and made available for public distribution.
