8,740 research outputs found
Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
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.Comment: 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 Press, 2013, pp. 86-91. ISBN
978-960-474-339-
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