Convex Analysis and Optimization with Submodular Functions: a Tutorial

Francis Bach (1, 2)

1 WILLOW - Models of visual object recognition and scene understanding
2 LIENS - Laboratoire d'informatique de l'école normale supérieure

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular functions is presented, in a self-contained way, with all results shown from first principles. A good knowledge of convex analysis is assumed.

Mots clés: Submodular functions; convex optimization; combinatorial optimization

Domaines: Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]; Machine Learning [stat.ML]

Francis Bach. Convex Analysis and Optimization with Submodular Functions: a Tutorial. 2010. ⟨hal-00527714v2⟩