Mathematical Sciences: Optimization Problems in Function Spaces

本项目将研究设计和分析 求解大规模优化问题的算法 和非线性方程， 无穷维问题 目标包括发展 逐点拟牛顿法的统一理论， 无限维中的对称秩一方法 传统和逐点上下文，分析一类新的 在有限差分计算中使用步长的方法， 梯度作为一种工具，以避免局部极小值的问题， 简单光滑函数和小振幅、高 频率、噪声项和全局收敛算法， 无穷维问题 基础研究将应用于辐射问题 转移，微波器件的计算机辅助设计，以及 竞争系统优化的数值方法。

This project will study the design and analysis of algorithms for the solution of large scale optimization problems and nonlinear equations that arise from discretizations of infinite dimensional problems. The goals include development of a unifying theory for pointwise quasi-Newton methods, study of the symmetric rank one method in infinite dimensions in both the conventional and pointwise contexts, analysis of a new class of methods that use the step in finite difference computation of gradients as a tool to avoid local minima for problems that are sums of simple smooth functions and small amplitude, high frequency, noise terms, and globally convergent algorithms for infinite dimensional problems. The basic research will be applied to problems in radiative transfer, computer sided design of microwave devices, and numerical methods for optimization of competitive systems.