  We consider multidimensional optimization problems, which are formulated and
solved in terms of tropical mathematics. The problems are to minimize
(maximize) a linear or nonlinear function defined on vectors over an idempotent
semifield, and may have constraints in the form of linear equations and
inequalities. The aim of the paper is twofold: first to give a broad overview
of known tropical optimization problems and solution methods, including recent
results; and second, to derive a direct, complete solution to a new constrained
optimization problem as an illustration of the algebraic approach recently
proposed to solve tropical optimization problems with nonlinear objective
functions.
