Optimization on the range of a max-separable operator

摘要

The paper considers systems of so called max-separable equations, which are a generalization of the systems of (max, +)-linear equations. The considered systems have the form r_i(x) = max r_(ij)(x_j) = b_i, i ∈ I, where I = {1,...,m}, J = {1,...,n}, b ∈ R~m and r_(ij) : R~1 → R~1, i ∈ I, j ∈J are continuous strictly increasing functions of one variable. Let P(R) denote the range of operator R(x) = (r_1(x), ..., r_m(x)). Then P(R) consists of all right-hand sides of the considered system, for which the system is solvable.