%0 Journal Article
%T Transformation to a fixed domain in LP modelling for a class of optimal shape design problems
%J Iranian Journal of Numerical Analysis and Optimization
%I Ferdowsi University of Mashhad
%Z 2423-6977
%A Mehne, H.H.
%A Farahi, M. H.
%D 2019
%\ 03/01/2019
%V 9
%N 1
%P 1-16
%! Transformation to a fixed domain in LP modelling for a class of optimal shape design problems
%K Approximation
%K optimal shape design
%K Linear programming
%K measure theory
%R 10.22067/ijnao.v9i1.53910
%X 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.
%U https://ijnao.um.ac.ir/article_24736_778b8f32dcb1d6def0bc85c6d947f67f.pdf