Transformation to a fixed domain in LP modelling for a class of optimal shape design problems

• Main Authors: H. Hashemi Mehne, M. H. Farahi
• Format: Article
• Language: English
• Published: Ferdowsi University of Mashhad 2019-03-01
• Series: Iranian Journal of Numerical Analysis and Optimization
• Subjects: approximation; optimal shape design; linear programming; measure theory
• Online Access: https://ijnao.um.ac.ir/article_24736_778b8f32dcb1d6def0bc85c6d947f67f.pdf

A class of optimal shape design problems is studied in this paper. The boundary shape of a domain is determined such that the solution of the underlying partial differential equation matches, as well as possible, a given desired state. In the original optimal shape design problem, the variable domain is parameterized by a class of functions in such a way that the optimal design problem is changed to an optimal control problem on a fixed domain. Then, the resulting distributed control problem is embedded in a measure theoretical form, in fact, an infinite-dimensional linear programming problem. The optimal measure representing the optimal shape is approximated by a solution of a finite-dimensional linear programming problem. The method is evaluated via a numerical example.