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Continuous relaxation for discrete DC programming

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Abstract

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.

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Notes

  1. http://snap.stanford.edu/data/ For other real-world networks in this collection, we performed the same experiments, to obtain similar results.

  2. http://www.diku.dk/~pisinger/codes.html.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematical and Systems Engineering, Shizuoka University, Shizuoka, Japan

    Takanori Maehara

  2. RIKEN Center for Advanced Intelligence Project, Tokyo, Japan

    Takanori Maehara

  3. Department of Mathematical Informatics, University of Tokyo, Tokyo, Japan

    Naoki Marumo

  4. School of Business Administration, Tokyo Metropolitan University, Tokyo, Japan

    Kazuo Murota

Authors
  1. Takanori Maehara
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  2. Naoki Marumo
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  3. Kazuo Murota
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Correspondence to Takanori Maehara.

Additional information

A preliminary version of this paper is included in the Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015, Metz, May 13–15) — Part I, Advances in Intelligent Systems and Computing, vol.359, Springer, 2015, pp. 181–190.

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Maehara, T., Marumo, N. & Murota, K. Continuous relaxation for discrete DC programming. Math. Program. 169, 199–219 (2018). https://doi.org/10.1007/s10107-017-1139-2

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  • DOI: https://doi.org/10.1007/s10107-017-1139-2

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