Recently, a NSF grant was granted to Jon Lee on submodular optimization.
This award provides funding for the development and analysis of practical exact and approximation algorithms for general submodular optimization problems, by generalizing and extending mathematical-optimization and approximation methods that have been successful in specific application areas. Important application areas include redesigning environmental monitoring networks and Boolean quadratic optimization. Thus far, general techniques for submodular optimization have been developed with the aim of providing provably good worst-case behavior. On the other hand, practical algorithms, not encumbered by theoretical requirements, have been developed and implemented for several special cases. This project is aimed at extending such success to the general case.
Algorithms will be instantiated and distributed as open-source software thus providing practical, general-purpose tools for attacking this ubiquitous problem class. With particular special cases defined through a black box (i.e., a function-evaluation subroutine), such software will have broad applicability across a variety of application areas, such as economics, machine learning, biodiversity conservation and statics. Moreover, the project is within the broader area of nonlinear discrete optimization, and it is natural to expect to have a broader influence within this important current topic.
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