Fundamentals in Discrete Convex Analysis
نویسنده
چکیده
“Discrete Convex Analysis” is aimed at establishing a novel theoretical framework for solvable discrete optimization problems by means of a combination of the ideas in continuous optimization and combinatorial optimization. The theoretical framework of convex analysis is adapted to discrete settings and the mathematical results in matroid/submodular function theory are generalized. Viewed from the continuous side, the theory can be classified as a theory of convex functions f : R → R that have additional combinatorial properties. Viewed from the discrete side, it is a theory of discrete functions f : Z → Z that enjoy certain nice properties comparable to convexity. Symbolically,
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