Extremal properties of tropical eigenvalues and solutions to tropical optimization problems

Understand

An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition.

• For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix.
• We examine the problem in the common setting of a general idempotent semifield.
• A complete direct solution in a compact vector form is obtained to this problem under fairly general conditions.