论文标题
使用特征功能的界面相关优化问题的模块化算法框架
A modularized algorithmic framework for interface related optimization problems using characteristic functions
论文作者
论文摘要
在本文中，我们考虑了一般优化问题的算法和收敛性，该算法和收敛性在图像分割，拓扑优化，流网络公式和表面重建方面具有广泛的应用。特别是，该问题着重于与接口相关的优化问题，在这些问题中，界面是由相应域的特征函数隐式描述的。在这种表示和离散化下，该问题被提出为离散的优化问题，其中目标函数相对于特征函数和与状态变量相对于特征函数和凸。我们表明，在这种结构下，基于替代最小化的迭代方案可以收敛到局部最小化器。进行广泛的数值示例以支持该理论。
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In particular, the problem focuses on interface related optimization problems where the interface is implicitly described by characteristic functions of the corresponding domains. Under such representation and discretization, the problem is then formulated into a discretized optimization problem where the objective function is concave with respect to characteristic functions and convex with respect to state variables. We show that under such structure, the iterative scheme based on alternative minimization can converge to a local minimizer. Extensive numerical examples are performed to support the theory.
