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We examine two multidimensional optimization problems that are formulated interms of tropical mathematics. The problems are to minimize nonlinear objectivefunctions, which are defined through the multiplicative conjugate vectortransposition on vectors of a finite-dimensional semimodule over an idempotentsemifield, and subject to boundary constraints. The solution approach isimplemented, which involves the derivation of the sharp bounds on the objectivefunctions, followed by determination of vectors that yield the bound. Based onthe approach, direct solutions to the problems are obtained in a compact vectorform. To illustrate, we apply the results to solving constrained Chebyshevapproximation and location problems, and give numerical examples.

Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints