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A complete closed-form solution to a tropical extremal problem. / Krivulin, Nikolai.
Advances in Computer Science: Proc. 6th Europ. Computing Conf. (ECC'12), Prague, Czech Republic, September 24-26, 2012. Vol. 5 of Recent Advances in Computer Engineering Series.. WSEAS - World Scientific and Engineering Academy and Society, 2012. стр. 528 стр., 146-151.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная
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TY - CHAP
T1 - A complete closed-form solution to a tropical extremal problem
AU - Krivulin, Nikolai
PY - 2012
Y1 - 2012
N2 - A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two other known problems by combining their objective functions into one general function and includes these problems as particular cases. A new solution approach is proposed based on the analysis of linear inequalities and spectral properties of matrices. The approach offers a comprehensive solution to the problem in a closed form that involves performing simple matrix and vector operations in terms of idempotent algebra and provides a basis for the development of efficient computational algorithms and their software implementation.
AB - A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two other known problems by combining their objective functions into one general function and includes these problems as particular cases. A new solution approach is proposed based on the analysis of linear inequalities and spectral properties of matrices. The approach offers a comprehensive solution to the problem in a closed form that involves performing simple matrix and vector operations in terms of idempotent algebra and provides a basis for the development of efficient computational algorithms and their software implementation.
KW - Idempotent semifield
KW - Finite-dimensional idempotent semimodule
KW - Functional on semimodule
KW - Linear inequality
KW - Spectrum of matrix
KW - Tropical extremal problem
M3 - Chapter
SN - 978-1-61804-126-5
SP - 528 стр., 146-151
BT - Advances in Computer Science: Proc. 6th Europ. Computing Conf. (ECC'12), Prague, Czech Republic, September 24-26, 2012. Vol. 5 of Recent Advances in Computer Engineering Series.
PB - WSEAS - World Scientific and Engineering Academy and Society
ER -
ID: 4576121