  We consider a multidimensional extremal problem formulated in terms of
tropical mathematics. The problem is to minimize a nonlinear objective
function, which is defined on a finite-dimensional semimodule over an
idempotent semifield, subject to linear inequality constraints. An efficient
solution approach is developed which reduces the problem to that of solving a
linear inequality with an extended set of unknown variables. We use the
approach to obtain a complete solution to the problem in a closed form under
quite general assumptions. To illustrate the obtained results, a
two-dimensional problem is examined and its numerical solution is given.
