In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight co...

the aim of this paper is to study the categorical relations betweenmatroids, goetschel-voxman’s fuzzy matroids and shi’s fuzzifying matroids.it is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. the category of matroids can be embedded in that offuzzifying matroids as a simul...