(Colloquium) Satoru Iwata, Submodular Optimization and Approximation Algorithms

Submodular functions are discrete analogues of convex functions. Examples include cut capacity functions, matroid rank functions, and entropy functions. Submodular functions can be minimized in polynomial time, which provides a fairly general framework of efficiently solvable combinatorial optimization problems. In contrast, the maximization problems are NP-hard and several approximation algorithms have been developed so far.
In this talk, I will review the above results in submodular optimization and present recent approximation algorithms for combinatorial optimization problems described in terms of submodular functions.