2022/03/14 by Beniamin Bogosel, Bogosel, Beniamin · 2 citations
Computer Science · Engineering · Mathematics · #49Q10 #52A27 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · doi:10.48550/arxiv.2203.06981
openalex publication_date 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.