[Question Set 1] Submodular functions: Definitions, examples and mathematical
operations
[Question Set 2] Matroids, submodular functions and polyhedral theory
[Question Set 3] Minimization of submodular functions
[Question Set 4] Maximization of submodular functions
[Question Set 5] Submodularity and randomness
Class Videos (can be downloaded from)
Reference Books
A. Schrijver. Combinatorial Optimization: Polyhedra and Efficiency, volume A,B,C. 2003. Springer-Verlag.
S. Fujishige. Submodular Functions and Optimization, 2nd Edition, Volume 58, 2005. Elsevier
M. Grotschel, L. Lovasz, and A. Schrijver. Geometric Algorithms and Combinatorial Optimization, volume 2 of Algorithms and Combinatorics, 2nd edition, 1993. Springer-Verlag.
G. L. Nemhauser, L. A. Wolsey. Integer and Combinatorial Optimization. 1999. Wiley
D.M Topkis. Supermodularity and Complementarity. 1998. Princeton University Press
F. Bach. Learning with submodular functions: A convex optimization perspective. 2013. Foundations and Trends in Machine Learning 6 (2-3), 145-373
K. Murota. Discrete Convex Analysis. 2003. SIAM.
Reference Articles
L. Lovasz. Submodular functions and convexity.1983. Mathematical Programming: The State of Art. 235-257.
G. L. Nemhauser, L. A. Wolsey and M. L. Fisher. An analysis of approximations for maximizing submodular set functions. 1978. Mathematical Programming. volume 14, 265-294.
F. Bach. Submodular functions: from discrete to continuous domains. 2019. Mathematical Programming. volume 175, 419-459
Reference Courses
Jeff Bilmes: Submodular Functions, Optimization, and Applications to Machine Learning https://people.ece.uw.edu/bilmes/classes/ee563/ee563_fall_2020
Michel Goemans. Advanced Combinatorial Optimization https://math.mit.edu/~goemans/18455-2020SP.html
J. Vondrak. Polyhedral techniques in combinatorial optimization https://theory.stanford.edu/~jvondrak/CS369P/CS369P.html