TY - JOUR
T1 - A Modularized Algorithmic Framework for Interface Related Optimization Problems Using Characteristic Functions
AU - Wang , Dong
AU - Zeng , Shangzhi
AU - Zhang , Jin
AU - Zhang , Ning
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 437
EP - 462
PY - 2025
DA - 2025/05
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0082
UR - https://global-sci.org/intro/article_detail/nmtma/24071.html
KW - Interface problems, thresholding, characteristic function, convergence analysis.
AB - <p style="text-align: justify;">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.</p>