When you referThank you very much for your consideration to refer to our papers. Please cite the following papers if appropriate.
Book: Discrete Convex Analysis
- K. Murota (2003): Discrete Convex Analysis. SIAM Monographs on Discrete Mathematics and Applications, Vol.10, Society for Industrial and Applied Mathematics.
- N. Tsuchimura, S. Moriguchi, and K. Murota (2013): Discrete convex optimization solvers and demonstration softwares, Transactions of the Japan Society for Industrial and Applied Mathematics, Vol. 23, No.2, pp. 233-252. (in Japanese) [ pdf ]
Continuous relaxation method for L-convex function minimization
- S. Moriguchi and N. Tsuchimura (2009): Discrete L-convex functions minimization based on continuous relaxation, Pacific Journal of Optimization, Vol. 5, No.2, pp. 227-236.
Continuous relaxation method for M-convex function minimization
- S. Moriguchi, A. Shioura, and N. Tsuchimura (2011): M-convex function minimization by continuous relaxation approach ---proximity theorem and algorithm---, SIAM Journal on Optimization, 21 (3), pp. 633-668.
Scaling method for M-convex function minimization
- S. Moriguchi, K. Murota, and A. Shioura (2002): Scaling algorithms for M-convex function minimization, IEICE Transactions on Fundamentals E85-A, pp. 922-929.
Surveys and introduction
- K. Murota (1999): Discrete convex analysis -- Exposition on conjugacy and duality, in Graph Theory and Combinatorial Biology (eds. L. Lovasz, A. Gyarfas, G. Katona, A. Recski, L. Szekely) Bolyai Society Mathematical Studies, Vol. 7, 1999, pp. 253-278
- K. Murota (2000): Algorithms in discrete convex analysis, IEICE Transactions on Systems and Information, E83-D, 344-352.
- K. Murota (2001): L-convex functions and M-convex functions, Encyclopedia of Optimization, P. M. Pardalos and C. A. Floudas, eds., Kluwer, pp.111-118
- K. Murota (2009): Recent developments in discrete convex analysis, in: W. Cook, L. Lovasz and J. Vygen, eds., Research Trends in Combinatorial Optimization, Bonn 2008, Springer-Verlag, Berlin, 2009, Chapter 11, pp.219-260.
- Extensions and ramifications of discrete convexity concepts [ slide ] by Kazuo Murota at Hausdorff Institute of Mathematics, Bonn, Trimester Program, Combinatorial Optimization, October 6, 2015.
- DC programming in discrete convex analysis [ slide ] by Kazuo Murota at Institute of Mathematics and Applications, February 24, 2015.
- Discrete Convex Analysis: Basics, DC programming, and submodular welfare algorithm [ slide , video ] by Kazuo Murota at NIPS - DISCML workshop, Lake Tahoe, December 9, 2013.
- Introduction to discrete convex analysis [slide / video ] by Kazuo Murota at Modern Aspects of Submodularity, Georgia Institute of Technology, March 19-22, 2012.
- Minimization and maximization algorithms in discrete convex analysis [slide / video ] by Kazuo Murota at Modern Aspects of Submodularity, Georgia Institute of Technology, March 19-22, 2012.
- Minimization and maximization algorithms in discrete convex analysis [ video ] by Satoru Fujishige at NIPS Workshop, Discrete Optimization in Machine Learning, Lake Tahoe, December 7, 2012.
- Submodular Function Minimization [ video ] by Satoru Iwata at NIPS Workshop, Discrete Optimization in Machine Learning, Whistler, December, 2010.
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