2009/02/18 by Jimmy Lamboley, Arian Novruzi, Lamboley, Jimmy +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Topology Optimization in Engineering #math.OC
paper · pdf · doi:10.48550/arxiv.0902.3062
arxiv created 2009/02/18 · openalex publication_date 2009/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we focus on the following general shape optimization problem: min\J(\Om), \Om convex, \Om∈\mathcal Sad\, where \mathcal Sad is a set of 2-dimensional admissible shapes and J:Sad→\R is a shape functional. Using a specific parameterization of the set of convex domains, we derive some extremality conditions (first and second order) for this kind of problem. Moreover, we use these optimality conditions to prove that, for a large class of functionals (satisfying a concavity like property), any solution to this shape optimization problem is a polygon.