Mathematical Sciences: Approximation Theory for Variational Problems with Applications to Random Composites and Stochastic Optimization Problems

本研究涉及的近似理论， 变分优化问题及其应用 一个主要 研究的努力将用于开发一种 定量理论，这将是更直接适用于一个 数字环境，并将提供一种计算方法， 误差估计 特别令人感兴趣的是， 将理论应用于随机环境，包括计算机 实施解决方案。 三个应用领域 在本项目中被挑选出来进行详细研究： 随机最优化问题，估计理论 统计学和随机算子方程， 或者流过随机的复合材料。 这项研究属于应用数学的一般领域 在统计学理论中的应用

This research is concerned with an approximation theory for variational (optimization) problems and its application. A major effort of the research will go to the development of a quantitative theory that would be more directly applicable in a numerical environment and would provide a means for calculating error estimates. Of particular interest is the application of the theory to a stochastic environment, including the computer implementation of solution procedures. Three application areas have been singled out for detailed study in this project: stochastic optimization problems, estimation theory in statistics, and random operator equations that model conductivity or flow through random composite materials. The research is in the general area of applied mathematics with applications to the theory of statistics.