Numeric Methods for Nonlinear Optimization

本项目的目的是开发求解大规模无约束优化问题的数值方法。将特别注意动态调整变量的战略，以及研究跨音速流动、神经元网络和气象学等领域出现的问题的结构。将开发新的预条件与离散截断牛顿方法结合使用，并将该方法的性能与有限内存和分区拟牛顿方法的性能进行比较。该项目还将研究分解原理，该原理允许将大型非线性问题作为一系列更简单的问题来解决。将开发用于解决非常大的非线性问题的有限内存的BFGS代码，并向公众分发。

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.