Mathematical Programming

, Volume 169, Issue 1, pp 199–219 | Cite as

Continuous relaxation for discrete DC programming

  • Takanori Maehara
  • Naoki Marumo
  • Kazuo Murota
Full Length Paper Series B


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 



This work is supported by JSPS KAKENHI Grant Numbers 26280004 and 16K16011, by The Mitsubishi Foundation, by CREST, JST, and by JST, ERATO, Kawarabayashi Large Graph Project.


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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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