2017/02/02 by Takayuki Okuno, Okuno, Takayuki, Yoshiko Ikebe +1
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1702.00553
openalex publication_date 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.