Monotone structure in discrete-event systems
Monotone structure in discrete-event systems
Mathematical Programming: Series A and B
Multimodularity, Convexity, and Optimization Properties
Mathematics of Operations Research
Submodular functions, matroids, and certain polyhedra
Combinatorial optimization - Eureka, you shrink!
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10
On Steepest Descent Algorithms for Discrete Convex Functions
SIAM Journal on Optimization
Discrete-Event Control of Stochastic Networks: Multimodularity and Regularity (Lecture Notes in Mathematics)
On the Convergence Rate for Stochastic Approximation in the Nonsmooth Setting
Mathematics of Operations Research
ACM Transactions on Modeling and Computer Simulation (TOMACS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a unimodular coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the literature of multimodular functions should be rectified, and a discrete separation theorem holds for multimodular functions.