  According to the Kouchnirenko formula, the Milnor number of a generic
isolated singularity with given Newton polyhedron is equal to the alternating
sum of certain volumes associated to the Newton polyhedron. In this paper we
obtain a non-negative analogue (i.e. without negative summands) of the
Kouchnirenko formula. The analogue relies on the non-negative formula for the
monodromy operator from arXiv:1405.5355 and formulas for the Milnor number from
arXiv:math/9901107 . As an application we give a criterion for the Arnold's
monotonicity problem (1982-16) in arbitrary dimension, which leads to complete
solution in dimension up to $4$. The latter relies on the classification of
vanishing local h-polynomial in dimension $2$ from arXiv:1909.10843 and
contains examples which differ dramatically from the ones which arise in
dimension up to $3$ (see arXiv:1705.00323 ). Some of the $4$-dimensional
examples were first described in arXiv:1309.0630 in the context of the local
monodromy conjecture.
