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Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints. / Krivulin, Nikolai; Karel, Zimmermann.
Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013. WSEAS - World Scientific and Engineering Academy and Society, 2013. стр. 242 стр., 86-91.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная
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TY - CHAP
T1 - Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
AU - Krivulin, Nikolai
AU - Karel, Zimmermann
PY - 2013
Y1 - 2013
N2 - We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finite-dimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, which involves the derivation of the sharp bounds on the objective functions, followed by determination of vectors that yield the bound. Based on the approach, direct solutions to the problems are obtained in a compact vector form. To illustrate, we apply the results to solving constrained Chebyshev approximation and location problems, and give numerical examples.
AB - We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finite-dimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, which involves the derivation of the sharp bounds on the objective functions, followed by determination of vectors that yield the bound. Based on the approach, direct solutions to the problems are obtained in a compact vector form. To illustrate, we apply the results to solving constrained Chebyshev approximation and location problems, and give numerical examples.
KW - idempotent semifield
KW - tropical optimization problem
KW - boundary constraint
KW - chebyshev location problem
KW - chebyshev approximation
M3 - Chapter
SN - 978-960-474-339-1
SP - 242 стр., 86-91
BT - Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013
PB - WSEAS - World Scientific and Engineering Academy and Society
ER -
ID: 4651328