@article {
author = {Mehne, H.H. and Farahi, M. H.},
title = {Transformation to a fixed domain in LP modelling for a class of optimal shape design problems},
journal = {Iranian Journal of Numerical Analysis and Optimization},
volume = {9},
number = {1},
pages = {1-16},
year = {2019},
publisher = {Ferdowsi University of Mashhad},
issn = {2423-6977},
eissn = {2423-6969},
doi = {10.22067/ijnao.v9i1.53910},
abstract = {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.},
keywords = {Approximation,optimal shape design,Linear programming,measure theory},
url = {https://ijnao.um.ac.ir/article_24736.html},
eprint = {https://ijnao.um.ac.ir/article_24736_778b8f32dcb1d6def0bc85c6d947f67f.pdf}
}