Department of Mathematics

Indian Institute of Science

Bangalore 560 012






Deeparnab Chakrabarty
Affiliation : Microsoft research, Bangalore

Subject Area






Department of Mathematics, Lecture Hall I




03:30 - 04:30 PM




February 26, 2016 (Friday)



"Understanding Wolfe’s Heuristic: Submodular Function Minimization 
and Projection onto Polytopes"


Owing to several applications in large scale learning and vision problems, fast submodular function minimization (SFM) has become a very important problem. Theoretically, unconstrained SFM is polynomial time solvable, however, these algorithms are not practical. In 1976, Wolfe proposed a heuristic for projection onto a polytope, and in 1980, Fujishige showed how Wolfe's heuristic can be used for SFM. For general submodular functions, this Fujishige-Wolfe heuristic seems to have the best empirical performance. Despite its good practical performance, very little is known about Wolfe's projection algorithm theoretically. In this talk, I will describe the first analysis which proves that the heuristic is polynomial time for bounded submodular functions. Our work involves the first convergence analysis of Wolfe’s projection heuristic, and proving a robust version of Fujishige’s reduction theorem.