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Submodular Optimization for Smooth Convergence
2015Smooth convergence ensures that the networked nodes converge to their desired states with minimal delay and error in their intermediate states. A submodular optimization approach to smooth convergence in networked systems is presented in this chapter. The approach is based on identifying connections between the system dynamics and the statistics of a ...
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Submodular Functions: Optimization and Approximation
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010), 2011Submodular functions are discrete analogue of convex functions, arising in various fields of applied mathematics including game theory, information theory, and queueing theory. This survey aims at providing an overview on fundamental properties of submodular functions and recent algorithmic developments of their optimization and approximation.
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A Submodular Optimization Problem with Side Constraints
Mathematics of Operations Research, 1996In this paper we consider the general problem of optimizing over the intersection of a submodular base polyhedron and an affine space. An example is the following flow problem defined on a capacitated network: We wish to send a commodity from locations in a producing country to locations in a number of client countries so as to simultaneously maximize
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Dilworth’s Completion, Submodular Functions, and Combinatorial Optimization
1990The motivation behind Dilworth’s investigation in [5] is the question whether a lattice can be imbedded into a geometric lattice. This paper concentrates on quasimodular point lattices, i. e., point lattices L of finite length such that all maximal chains of L share the same length and the rank function f of L satisfies the weakened submodularity ...
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