Continuous Relaxation for Discrete DC Programming
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 optimal solution of the continuous relaxation coincides with the original discrete problem. The proposed method is demonstrated for the degree-concentrated spanning tree problem.
KeywordsConvex Function Span Tree Span Tree Problem Discrete Optimization Problem Submodular Function
Unable to display preview. Download preview PDF.
- 3.Iyer, R., Jegelka, S., Bilmes, J.: Fast semidifferential-based submodular function optimization. In: Proceedings of the 30th International Conference on Machine Learning, pp. 855–863 (2013)Google Scholar
- 4.Kawahara, Y., Washio, T.: Prismatic algorithm for discrete D.C. programming problem. In: Proceedings of the 25th Annual Conference on Neural Information Processing Systems, pp. 2106–2114 (2011)Google Scholar
- 5.Kobayashi, Y.: The complexity of maximizing the difference of two matroid rank functions. METR2014-42, University of Tokyo (2014)Google Scholar
- 7.Lemke, P.: The maximum leaf spanning tree problem for cubic graphs is NP-complete. IMA Preprint Series #428, University of Minnesota (1988)Google Scholar
- 8.Le-Thi, H.A.: DC Programming and DCA, http://www.lita.univ-lorraine.fr/~lethi/index.php/en/research/dc-programming-and-dca.html (retrieved at February 23, 2015)
- 9.Maehara, T., Murota, K.: A framework of discrete DC programming by discrete convex analysis. Mathematical Programming (2014), http://link.springer.com/article/10.1007
- 13.Murota, K.: Recent developments in discrete convex analysis. In: Cook, W., Lovász, L., Vygen, J. (eds.) Research Trends in Combinatorial Optimization, ch. 11, pp. 219–260. Springer, Berlin (2009)Google Scholar
- 14.Narasimhan, M., Bilmes, J.: A submodular-supermodular procedure with applications to discriminative structure learning. In: Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence, pp. 404–412 (2005)Google Scholar
- 15.Tanenbaum, A.S.: Computer Networks, 5th edn. Prentice Hall, Upper Saddle River (2010)Google Scholar
- 17.Hoang, T.: D.C. optimization: Theory, methods and algorithms. In: Horst, R., Pardalos, P.M. (eds.) Handbook of Global Optimization, pp. 149–216. Kluwer Academic Publishers, Dordrecht (1995)Google Scholar