论文标题
凸组之间的数值形状优化
Numerical shape optimization among convex sets
论文作者
论文摘要
本文提出了一个新的离散框架，用于近似解决方案以在凸度约束下塑造优化问题。基于支持函数或量规函数的数值方法可以保证生成离散的凸形形状，并且可以使用标准优化软件易于实现。该框架可以处理从几何数量到功能的各种目标功能，具体取决于部分微分方程。使用支撑功能处理宽度或直径约束。功能取决于凸体及其极性体，可以使用统一的框架来处理。
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate discrete convex shapes and is easily implementable using standard optimization software. The framework can handle various objective functions ranging from geometric quantities to functionals depending on partial differential equations. Width or diameter constraints are handled using the support function. Functionals depending on a convex body and its polar body can be handled using a unified framework.
