A tropical extremal problem with nonlinear objective function and linear inequality constraints

Understand

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.