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Volume 16, Issue 4
A Review of Theoretical Measure Approaches in Optimal Shape Problems

Alireza Fakharzadeh Jahromi & Hajar Alimorad

Int. J. Numer. Anal. Mod., 16 (2019), pp. 543-574.

Published online: 2019-02

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  • Abstract

Some optimal shape design problems lack classical solutions, or at least, the existence of such solutions is far from being straightforward. In such cases, to obtain an optimal solution, a variety of methods have been employed. In this study, we review the works that used measures which can basically be divided in two groups: using Young measures and embedding process (Shape-measure method). We also survey the advantages and disadvantages of these two methods and investigate their improved version in the presented works and applications.

  • Keywords

Young measure, radon measure, atomic measure, optimal shape, shape-measure, linear programming problem, relaxed problem.

  • AMS Subject Headings

49M20, 49J20, 90C90, 49M25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

a_fakharzadeh@sutech.ac.ir (Alireza Fakharzadeh Jahromi)

hajaralimorad@yahoo.com (Hajar Alimorad)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-543, author = {Jahromi , Alireza Fakharzadeh and Alimorad , Hajar}, title = {A Review of Theoretical Measure Approaches in Optimal Shape Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2019}, volume = {16}, number = {4}, pages = {543--574}, abstract = {

Some optimal shape design problems lack classical solutions, or at least, the existence of such solutions is far from being straightforward. In such cases, to obtain an optimal solution, a variety of methods have been employed. In this study, we review the works that used measures which can basically be divided in two groups: using Young measures and embedding process (Shape-measure method). We also survey the advantages and disadvantages of these two methods and investigate their improved version in the presented works and applications.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13014.html} }
TY - JOUR T1 - A Review of Theoretical Measure Approaches in Optimal Shape Problems AU - Jahromi , Alireza Fakharzadeh AU - Alimorad , Hajar JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 543 EP - 574 PY - 2019 DA - 2019/02 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13014.html KW - Young measure, radon measure, atomic measure, optimal shape, shape-measure, linear programming problem, relaxed problem. AB -

Some optimal shape design problems lack classical solutions, or at least, the existence of such solutions is far from being straightforward. In such cases, to obtain an optimal solution, a variety of methods have been employed. In this study, we review the works that used measures which can basically be divided in two groups: using Young measures and embedding process (Shape-measure method). We also survey the advantages and disadvantages of these two methods and investigate their improved version in the presented works and applications.

Jahromi , Alireza Fakharzadeh and Alimorad , Hajar. (2019). A Review of Theoretical Measure Approaches in Optimal Shape Problems. International Journal of Numerical Analysis and Modeling. 16 (4). 543-574. doi:
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