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Recent Developments in Discrete Convex Analysis

In: Research Trends in Combinatorial Optimization

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  • Kazuo Murota

    (University of Tokyo, Department of Mathematical Informatics, Graduate School of Information Science and Technology)

Abstract

Summary This paper describes recent developments in discrete convex analysis. Particular emphasis is laid on natural introduction of the classes of L-convex and M-convex functions in discrete and continuous variables. Expansion of the application areas is demonstrated by recent connections to submodular function maximization, finite metric space, eigenvalues of Hermitian matrices, discrete fixed point theorem, and matching games.

Suggested Citation

  • Kazuo Murota, 2009. "Recent Developments in Discrete Convex Analysis," Springer Books, in: William Cook & László Lovász & Jens Vygen (ed.), Research Trends in Combinatorial Optimization, chapter 11, pages 219-260, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-76796-1_11
    DOI: 10.1007/978-3-540-76796-1_11
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