Books, Surveys, and Tutorials

Books

• K. Murota (2003): Discrete Convex Analysis. SIAM Monographs on Discrete Mathematics and Applications, Vol.10, Society for Industrial and Applied Mathematics.
• K. Murota, and A. Shioura (2013): Discrete Convex Analysis and Optimization Algorithms (in Japanese). Asakura Publishing Co., Tokyo.

Surveys

• 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.
• K. Murota (2015): Discrete convex analysis, Supplemantary material for Summer School (September 21--25, 2015) at Hausdorff Institute of Mathematics, Trimester Program, Combinatorial Optimization
• K. Murota (2016): Discrete convex analysis: A tool for economics and game theory, Journal of Mechanism and Institution Design, Vol.1 (2016), No.1, 151-273.

• Tutorial Slides/Videos

  • Submodular Function Minimization [ video ] by Satoru Iwata at NIPS Workshop, Discrete Optimization in Machine Learning, Whistler, December, 2010.
  • 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.
  • 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 [ video ] by Satoru Fujishige at NIPS Workshop, Discrete Optimization in Machine Learning, Lake Tahoe, December 7, 2012.
  • Discrete Convex Analysis: Basics, DC programming, and submodular welfare algorithm [ slide , video ] by Kazuo Murota at NIPS - DISCML workshop, Lake Tahoe, December 9, 2013.
  • Extensions and ramifications of discrete convexity concepts [ slide ] by Kazuo Murota at Hausdorff Institute of Mathematics, Bonn, Trimester Program, Combinatorial Optimization, October 6, 2015.
  • Discrete Convex Analysis I: Concepts of Discrete Convex Functions, Discrete Convex Analysis II: Properties of Discrete Convex Functions, Discrete Convex Analysis III: Algorithms for Discrete Convex Functions [ slide I , slide II , slide III ] by Kazuo Murota, RIMS Summer School (COSS 2018), Kyoto, July 2018.