Relaxation theorems and necessary optimality conditions for semiconvex multidimensional control problems

半凸多维控制问题的松弛定理和必要的最优性条件

• 批准号: 169104499
• 负责人: Privatdozent Dr. Marcus Wagner
• 金额: --
• 依托单位: Mathematics Institute for Geometry and Applications (MATHGEOM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/169104499?language=en
• 关键词: Relaxation; theorems; necessary; optimality; conditions

Up to now, the proof of Pontryagin's maximum principle for multidimensional control problems is closely related to the convexity or the convex relaxability of integrand and control domain. In order to overcome this limitation, the proposal aims to derive first-order optimality conditions for multidimensional control problems with first-order PDE's involving either polyconvex or quasiconvex data from the outset or requiring nonconvex relaxation. Proof techniques, which combine elements of polyconvex analysis with discretization methods and properties of gradient Young measures, will be applied. The connections between the proof of necessary optimality conditions and the semiconvex relaxation, which is mandatory for problems in the "vectorial" case, shall be systematically investigated.

迄今为止，多维控制问题的庞特里亚金极大原理的证明与被积域和控制域的凸性或凸松弛性密切相关。为了克服这一限制，该提案旨在推导一阶PDE多维控制问题的一阶最优性条件，该问题从一开始就涉及多凸或拟凸数据或需要非凸松弛。证明技术，它结合了多凸分析的元素与离散化方法和梯度杨测度的性质，将被应用。必要最优性条件的证明与半向量松弛之间的联系，对于“向量”情况下的问题是必需的，将被系统地研究。

项目成果

OPTIMAL CONTROL OF THE BIDOMAIN SYSTEM (III): EXISTENCE OF MINIMIZERS AND FIRST-ORDER OPTIMALITY CONDITIONS

• DOI: 10.1051/m2an/2012058
• 发表时间: 2013-07-01
• 期刊: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
• 影响因子: 1.9
• 作者: Kunisch, Karl;Wagner, Marcus
• 通讯作者: Wagner, Marcus

Multimodal image registration by elastic matching of edge sketches via optimal control

通过最优控制对边缘草图进行弹性匹配的多模态图像配准

• DOI: 10.3934/jimo.2014.10.567
• 发表时间: 2014
• 期刊: Journal of Industrial and Management Optimization
• 影响因子: 1.3
• 作者: Angelov;Wagner
• 通讯作者: Wagner