An Optimization-Based Methodology for Computer- Aided Design

基于优化的计算机辅助设计方法

• 批准号: 9302926
• 负责人: Elijah Polak
• 金额: $ 16.5万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-08-15 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302926&HistoricalAwards=false
• 关键词: Optimization; Based; Methodology; Computer; Aided

9302926 Polak This is a three year proposal for research on the construction of efficient numerical methods, based on the concept of consistent approximations, for the solution of optimization problems arising in control, shape design, and integrated design of actively controlled structures. In particular, we will address the following issues: (i) the development of a general theory of algorithms based on consistent approximations for semi-infinite optimization, optimal control, and optimal shape design; (ii) the determination of the effects of the order and complexity of numerical integration formulae for ODE's and evolution on the computational efficiency of algorithms for the solution of optimal control problems, with control and state space constraints; (iii) the development of basic elements needed for the solution of shape optimization problems via consistent approximations, such as consistent optimality functions for shape optimization problems and their discrete approximations, numerical integration methods for PDE's that satisfy certain uniformity conditions, as well as subalgorithms that can cope efficiently with the very high dimensional problems that result from discretization. ***

9302926 Polak这是一个为期三年的建议，研究建设有效的数值方法，一致的近似的概念的基础上，为解决优化问题所产生的控制，形状设计和集成设计的主动控制结构。 特别是，我们将解决以下问题：（i）发展的一般理论的算法一致的近似半无限优化，最优控制和最优形状设计的基础上;（二）确定常微分方程和演化的数值积分公式的阶数和复杂性对最优控制解算法的计算效率的影响问题，具有控制和状态空间约束;（iii）开发通过一致逼近解决形状优化问题所需的基本元素，例如形状优化问题的一致最优性函数及其离散逼近，满足某些一致性条件的PDE的数值积分方法，以及子算法，可以有效地科普非常高维的问题，从离散化。 ***