An Optimization-Based Methodology for Computer- Aided Design

9302926 Polak这是一项为期三年的研究计划，旨在基于一致近似的概念构建有效的数值方法，以解决主动控制结构的控制、形状设计和集成设计中出现的优化问题。特别是，我们将解决以下问题：(i)基于半无限优化，最优控制和最优形状设计的一致近似的一般算法理论的发展；（ii）确定ODE和演化的数值积分公式的顺序和复杂性对求解具有控制和状态空间约束的最优控制问题的算法的计算效率的影响；（iii）通过一致近似解决形状优化问题所需的基本要素的发展，例如形状优化问题的一致最优性函数及其离散近似，满足一定均匀性条件的PDE的数值积分方法，以及可以有效处理由离散化引起的非常高维问题的子算法。＊＊＊

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. ***