Adaptive multilevel SQP-methods for PDAE-constrained optimization with restrictions on control and state. Theory and Applications

用于具有控制和状态限制的 PDAE 约束优化的自适应多级 SQP 方法。

• 批准号: 25227538
• 负责人: Professor Dr. Jens Lang
• 金额: --
• 依托单位: Arbeitsgruppe Nichtlineare Optimierung
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/25227538?language=en
• 关键词: Adaptive; multilevel; SQP; methods; PDAE

To explore the fundamental scientific issues of high dimensional complex engineering applications such as optimal control problems with time-dependent partial differential algebraic equations (PDAEs) scalable numerical algorithms are requested. This means that the work necessary to solve increasingly larger problems should grow all but linearly - the optimal rate. In this joint project we want to combine modern solution strategies to solve time-dependent systems of partial differential algebraic equations such as adaptive multilevel finite elements methods and error-controlled linearly implicit time integrators of higher order with state-of-the-art optimization techniques including inexact nonmonoton SQP-methods with an efficient handling of control and state constraints by interior-point or semismooth Newton strategies, where the optimization method controls the inexactness and accuracy of the PDAE-solver in an adaptive way. Adaptivity based on a posteriori error estimates enables us to judge the quality of the numerical approximations and used models to determine appropriate strategies to improve the accuracy of the overall optimization process. Successful adaptive methods lead to substantial savings in computer time and memory requirements. They can mean the difference between getting an answer or not to the optimization problem considered.An optimal boundary control problem of the cooling down process of glass modelled by radiative heat transfer and thermo-mechanical coupling between elastic deformation and heat transfer, and an optimal control of dopant s redistribution in silicon serve as showcase engineering applications where restrictions on state and control variables are essential.

为了探索高维复杂工程应用的基本科学问题，例如与时间相关的部分差分代数方程（PDAE）可扩展的数值算法。这意味着解决越来越大的问题所需的工作应以线性的方式增长 - 最佳速度。在这个联合项目中，我们希望结合现代解决方案策略，以求解部分差分代数方程的时间依赖时间系统，例如自适应多级有限元方法和错误控制的较高级别的较高阶段的较高阶段的时间集成器以及最先进的优化技术以及与不存在的非ext semional semifience semifience nortal semielist semistion semistion semistion semistion semistion semistion semistion semistion squp-methods，并有效地构造有效的策略，并构成有效的方法优化方法以自适应方式控制PDAE-Solver的不精确度和准确性。基于后验错误估计的适应性使我们能够判断数值近似值的质量，并使用模型来确定适当的策略以提高整体优化过程的准确性。成功的自适应方法可以大大节省计算机时间和内存需求。它们可能意味着要获得答案或不考虑优化问题之间的区别。通过辐射传热和弹性变形和传热传递与热机电耦合建模的玻璃的最佳边界控制问题，以及对硅胶在硅的重新分配的最佳控制，作为对国家和控制的限制，是对国家和控制的限制。