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

Iranian Journal of Numerical Analysis and Optimization

卷:9

H. Hashemi Mehne¹  M. H. Farahi² 

[1] Aerospace Research Institute, Tehran,;

[2] Ferdowsi University of Mashhad, Mashhad, Iran.;

关键词: approximation;    optimal shape design;    linear programming;    measure theory;   

DOI  :  10.22067/ijnao.v9i1.53910

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown