Discrete Convex Analysis
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Author(s): K. Murota
Publisher: SIAM
ISBN: 0898715407
Format: hardback
389pp
Price: $111.00
Review Date: 18 September 2003
Review: Here Kazuo Murota provides a new unified theoretical framework for solvable discrete optimisation problems through mathematical studies of convex functions with combinatorial structures or discrete functions with convexity structures. This theory is expanded by developing efficient algorithms and applications to a number of different disciplines, such as matrix theory, operations research and economics. The book shows the unexpected link between matroid theory and mathematical economics and sets out in detail a deeper connection between matrices and matroids than that given in most standard textbooks. There are chapters on: the central concepts of discrete convex analysis; convex functions with combinatorial structures; convex analysis, linear programming and integrality; M-convex sets and submodular set functions; M-convex functions; L-convex functions; conjugacy and duality; network flows; algorithms; the application to mathematical economics; and the application to systems analysis by mixed matrices.