Algebraic Solution of Tropical Polynomial Optimization Problems

We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with addition and invertible multiplication). The are to minimize objective functions given by analogues of multivariate Puiseux polynomials, subject box constraints variables. A technique for variable elimination is presented that converts original problem new one which removed constraint this modified. novel approach may be thought as an extension Fourier-Motzkin method systems linear inequalities ordered fields issue polynomial semifields. use develop procedure solve finite number iterations. includes two phases: backward forward substitution describe main steps procedure, discuss its computational complexity present numerical examples.