Abstract
We offer an overview on submodular optimization for both single- and multiple-objectives, with the moderate goal to highlight the different angles in interpreting submodularity and associated concepts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bach, F.: Learning with submodular functions: a convex optimization perspective. Found. Trends Mach. Learn. 6(2-3), 145–373 (2013)
Buchbinder, N., Feldman, M., Naor, J.S., Schwartz, R.: A tight linear time (1/2)-approximation for unconstrained submodular maximization. In: Foundations of Computer Science (FOCS), 2012 IEEE 53rd Annual Symposium on, pp. 649–658. IEEE, Piscataway (2012)
Calinescu, G., Chekuri, C., Pál, M., Vondrák, J.: Maximizing a submodular set function subject to a matroid constraint. In: Integer Programming and Combinatorial Optimization, pp. 182–196. Springer, Berlin (2007)
Choquet, G.: Theory of capacities. In: Annales de l’institut Fourier, vol. 5, pp. 131–295. Institut Fourier, Chartres (1954)
Crama, Y., Hammer, P.L.: Boolean Functions: Theory, Algorithms, and Applications. Cambridge University, Cambridge (2011)
Du, D.L., Li, Y., Xiu, N.H., Xu, D.C.: Simultaneous approximation of multi-criteria submodular function maximization. J. Oper. Res. Soc. China 2(3), 271–290 (2014)
Fujishige, S.: Submodular Functions and Optimization, vol. 58. Elsevier, Boston (2005)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Lovász, L.: Submodular functions and convexity. In: Mathematical Programming The State of the Art, pp. 235–257. Springer, New York (1983)
McCormick, S.T.: Submodular function minimization. Handbooks Oper. Res. Management Sci. 12, 321–391 (2005)
Owen, G.: Game Theory. Academic, San Diego (1995)
Topkis, D.M.: Supermodularity and Complementarity. Princeton University, Princeton (1998)
Vondrak, J.: Optimal approximation for the submodular welfare problem in the value oracle model. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 67–74. ACM, New York (2008)
Vondrák, J.: Symmetry and approximability of submodular maximization problems. SIAM J. Comput. 42(1), 265–304 (2013)
Acknowledgements
The first author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (No. 06446), and the Natural Science Foundation of China (NSFC) (No. 11771386 and No. 11728104). The second author’s research is supported by the NSFC (No. 11771386 and No. 11728104). The third author’s research was supported by the NSFC (No. 11501412).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Du, D., Han, Q., Wu, C. (2019). An Overview of Submodular Optimization: Single- and Multi-Objectives. In: Du, DZ., Pardalos, P., Zhang, Z. (eds) Nonlinear Combinatorial Optimization. Springer Optimization and Its Applications, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-030-16194-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-16194-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16193-4
Online ISBN: 978-3-030-16194-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)