Mathematical Sciences: Iterative Methods for Equations and Optimization

小行星9321938 主要研究者将设计和分析线性和非线性方程的大型系统的算法，以及无限维问题离散化时出现的优化问题。 目标包括进一步发展一个新的多层次的方法紧凑的不动点问题，工作的非光滑紧凑的不动点问题，特别是那些产生的抛物控制问题的全局收敛方法，和分析的超规范收敛的某些方法的基础上的内部产品，特别是GMRES，CG，和原始对偶内点方法。 首席研究员还将继续研究非线性方程的优化和求解的特殊目的方法。这些方法针对的问题，如噪声函数的优化，微波器件的计算机辅助设计，和最佳控制。 大型方程组在科学计算中以多种方式出现。 这个项目是设计和分析在许多应用中出现的非常大的问题的类的有效的解决方案的方法。 在这个项目中研究的特定目标和算法是由应用驱动的，首席研究员与其他学科的科学家和工程师密切合作。 例如，在微波半导体器件的计算机辅助设计和制造中，如雷达和蜂窝通信中使用的放大器，主要研究者的工作已被纳入软件中，用于分析和优化工艺产量，设计更有效的器件，以及芯片的台架测试。在该软件的开发过程中，发现了一种新的算法，用于优化噪声函数，即其值被噪声或误差破坏的函数。工艺成品率模型通常具有该特征。 本项目的一个目标是继续噪声优化的工作。

9321938 Kelley The principal investigator will design and analyze algorithms for the large systems of linear and nonlinear equations and optimization problems that arise when infinite dimensional problems are discretized. Objectives include further development of a new multilevel method for compact fixed point problems, work on globally convergent methods for nonsmooth compact fixed point problems, particularly those that arise from parabolic control problems, and analysis of the sup-norm convergence of certain methods based on inner products, particularly GMRES, CG, and primal-dual interior point methods. The principal investigator will also continue work on special purpose methods for optimization and solution of nonlinear equations. These methods are directed at problems such as optimization of noisy functions, aomputer aided design of microwave devices, and optimal control. Large systems of equations arise in scientific computation in many ways. This project is to design and analyze efficient solution methods for classes of very large problems that arise in many applications. The particular objectives of and algorithms studied in this project are driven by applications and the principal investigator works closely with scientists and engineers in other disciplines. As an example, in computer aided design and manufacture of microwave semiconductor devices, such as the amplifiers used in radar and cellular communication, the principal investigator's work has been incorporated into software for analysis and optimization of process yield, design of more efficient devices, and bench testing of chips. In the course of the development of this software, a new algorithm was discovered for the optimization of noisy functions, that is, functions whose values are corrupted by noise or error. Process yield models often have that feature. One goal of the present project is to continue the work on noisy optimization.