  In this paper, we show that the subadditive dual of a feasible conic
mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover,
we show that this dual feasibility condition is equivalent to feasibility of
the conic dual of the continuous relaxation of the conic MIP. In addition, we
prove that all known conditions and other 'natural' conditions for strong
duality, such as strict mixed-integer feasibility, boundedness of the feasible
set or essentially strict feasibility imply that the subadditive dual is
feasible. As an intermediate result, we extend the so-called 'finiteness
property' from full-dimensional convex sets to intersections of
full-dimensional convex sets and Dirichlet convex sets.

Optimization and Control