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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 7, Page 1230 (Mi zvmmf10593)  

This article is cited in 2 scientific papers (total in 2 papers)

A theoretical measure technique for determining $3\mathrm{D}$ symmetric nearly optimal shapes with a given center of mass

H. D. Alimorad, A. J. Fakharzadeh

Shiraz University of Technology, Shiraz, Iran

Abstract: In this paper, a new approach is proposed for designing the nearly-optimal three dimensional symmetric shapes with desired physical center of mass. Herein, the main goal is to find such a shape whose image in $(r, \theta)$-plane is a divided region into a fixed and variable part. The nearly optimal shape is characterized in two stages. Firstly, for each given domain, the nearly optimal surface is determined by changing the problem into a measure-theoretical one, replacing this with an equivalent infinite dimensional linear programming problem and approximating schemes; then, a suitable function that offers the optimal value of the objective function for any admissible given domain is defined. In the second stage, by applying a standard optimization method, the global minimizer surface and its related domain will be obtained whose smoothness is considered by applying outlier detection and smooth fitting methods. Finally, numerical examples are presented and the results are compared to show the advantages of the proposed approach.

Key words: artificial control, center of mass, honey-bee-method, outlier detection, radon measure, symmetric three dimensional shape.

DOI: https://doi.org/10.7868/S004446691707002X

Full text: PDF file (29 kB)

English version:
Computational Mathematics and Mathematical Physics, 2017, 57:7, 1225–1240

Bibliographic databases:

UDC: 519.626
Received: 05.10.2014
Revised: 10.08.2015

Citation: H. D. Alimorad, A. J. Fakharzadeh, “A theoretical measure technique for determining $3\mathrm{D}$ symmetric nearly optimal shapes with a given center of mass”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1230; Comput. Math. Math. Phys., 57:7 (2017), 1225–1240

Citation in format AMSBIB
\by H.~D.~Alimorad, A.~J.~Fakharzadeh
\paper A theoretical measure technique for determining $3\mathrm{D}$ symmetric nearly optimal shapes with a given center of mass
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 7
\pages 1230
\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 7
\pages 1225--1240

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Alimorad H., “A New Approach For Determining Multi-Objective Optimal Control of Semilinear Parabolic Problems”, Comput. Appl. Math., 38:1 (2019)  crossref  mathscinet  isi  scopus
    2. Jahromi A.F., Alimorad H., “A Review of Theoretical Measure Approaches in Optimal Shape Problems”, Int. J. Numer. Anal. Model., 16:4 (2019), 543–574  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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