  In this paper, we consider a class of mixed integer programming problems
(MIPs) whose objective functions are DC functions, that is, functions
representable in terms of the difference of two convex functions. These MIPs
contain a very wide class of computationally difficult nonconvex MIPs since the
DC functions have powerful expressability. Recently, Maehara, Marumo, and
Murota provided a continuous reformulation without integrality gaps for
discrete DC programs having only integral variables. They also presented a new
algorithm to solve the reformulated problem. Our aim is to extend their results
to MIPs and give two specific algorithms to solve them. First, we propose an
algorithm based on DCA originally proposed by Pham Dinh and Le Thi, where
convex MIPs are solved iteratively. Next, to handle nonsmooth functions
efficiently, we incorporate a smoothing technique into the first method. We
show that sequences generated by the two methods converge to stationary points
under some mild assumptions.
