Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
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Ill-posed problems and multicriteria programming

Published: 08.04.2015

Authors: Greshilov A.A.

Published in issue: #2(38)/2015

DOI: 10.18698/2308-6033-2015-2-1367

Category: Aviation and Rocket-Space Engineering | Chapter: Innovation Technologies of Aerospace Engineering

Solving ill-posed problems by methods of multicriteria mathematical programming has been considered. Several methods of multicriteria mathematical programming (method of compression of acceptance region and goal programming) are used simultaneously allowing considering additional types of restrictions (nonnegativity of the solution, boundedness of solution) which must be met by evaluation of solution and which do not require definition of the regularization parameters necessary in the classical methods of regularization. When registering a small number of isotopes the merger of the two types of uranium-235 instant fission into one kind of division and two types of plutonium-239 fission into one kind of division is used. Simultaneously different variants of the nuclear explosion mechanism are considered. Determination of contributions of different fission kinds into the total activity of isotopes of krypton and xenon is performed by formation of a functional for a given moment of separation tq and time measurements t of functions Fl.

[1] Tikhonov A.N. Doklady Akademii nauk SSSR - Reports of the USSR Academy of Sciences. 1963. vol. 161. no. 3. pp. 501-504.
[2] Morozov V.A. Vychislitelnye metody I programmirovanie: Novye vychislitelnye tekhnologii - Computational Methods and Programming: New Computing Technologies, (Electron. Edition). 2003. vol. 4. pp. 130-141.
[3] Malioutov D.M. A Sparse Signal Reconstruction Perspective for Source Localization with Sensor Arrays. IEEE Transactions on Signal Processing, 2005. vol. 53. no. 8. pp. 3010-3022.
[4] Zhdanov A.I. Zhurnal vychislitelnoy matematiki i matematicheskoi fiziki RAN - Journal of Computational Mathematics and Mathematical Physics RAS, 2005, vol. 45, no. 11, pp. 1919-1927.
[5] Greshilov A.A. Nekorrektnye zadachi tsifrovoy obrabotki informatsii i signalov [Some Ill-Posed Problems of Digital Information and Signal Processing]. Moscow, Universitetskaya kniga; Logos Publ., 2009, 360 p.
[6] Greshilov A.A. Matematicheskie metodyprinyatiya resheniy: Uchebnoe posobie dlya vuzov [Mathematical Methods of Decision-Making: study book for higher school]. Moscow, BMSTU Publ., 2014, 645 p.
[7] Greshilov A.A., Lebedev A.L. Sposob identificatsii jadernogo vzriva po isotopam kriptona I ksenona. [A Method for Determining the Concentration of Inert Gas Isotope in the Mixture of Fission Products]. Patent № 2407039 Russian Federation, 2010, bulletin № 35, 21 p.
[8] Greshilov A.A., Tetukhin A.A Vestnic MGTU im. N.E. Baumana. Seria Estestvennye nauki - Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2003, no. 2, pp. 3-19.