Continuous relaxation for discrete DC programming

Full Length Paper Series B

DOI: 10.1007/s10107-017-1139-2

Cite this article as:
Maehara, T., Marumo, N. & Murota, K. Math. Program. (2017). doi:10.1007/s10107-017-1139-2


Discrete DC programming with convex extensible functions is studied. A natural approach for this problem is a continuous relaxation that extends the problem to a continuous domain and applies the algorithm in continuous DC programming. By employing a special form of continuous relaxation, which is named “lin-vex extension,” the produced optimal solution of the extended continuous relaxation coincides with the solution of the original discrete problem. The proposed method is demonstrated for the degree-concentrated spanning tree problem, the unfair flow problem, and the correlated knapsack problem.

Mathematics Subject Classification

90C27 Combinatorial optimization 

Funding information

Funder NameGrant NumberFunding Note
Japan Society for the Promotion of Science (JP)
  • KAKENHI 26280004
Japan Society for the Promotion of Science (JP)
  • 16K16011
Japan Science and Technology Agency
  • ERATO, Kawarabayashi Large Graph Project
Mitsubishi Foundation
    Core Research for Evolutional Science and Technology

      Copyright information

      © Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2017

      Authors and Affiliations

      1. 1.Department of Mathematical and Systems EngineeringShizuoka UniversityShizuokaJapan
      2. 2.RIKEN Center for Advanced Intelligence ProjectTokyoJapan
      3. 3.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan
      4. 4.School of Business AdministrationTokyo Metropolitan UniversityTokyoJapan

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