Structured convex optimization under submodular constraints

Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013

Volumn , Issue , 2013, Pages 459-468

  Nagano, Kiyohito ^a   Kawahara, Yoshinobu ^b  

^a FUTURE UNIVERSITY HAKODATE   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EXPERIMENT; CONTINUOUS OPTIMIZATION PROBLEMS; CONVEX OPTIMIZATION PROBLEMS; DIRECTED GRAPH STRUCTURES; MAXIMUM FLOW PROBLEMS; STRUCTURED CONVEX OPTIMIZATIONS; SUBMODULAR CONSTRAINTS; SUBMODULAR OPTIMIZATIONS;

ARTIFICIAL INTELLIGENCE;

CONVEX OPTIMIZATION;

EID: 84888147975     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (31)

1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993.
2. F. Bach. Structured sparsity-inducing norms through submodular functions. In Advances in Neural Information Processing Systems 23 (NIPS 2010), pages 118-126, 2010.
3. A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1): 183-202, 2009.
4. A. Chambolle and J. Darbon. On total variation minimization and surface evolution using parametric maximal flows. International Journal of Computer Vision, 84(3), 2009.
5. P. Boldi et al. Laboratory for Web Algorithmics. http://law.di.unimi.it/ datasets.php.
6. L. Fleischer and S. Iwata. A push-relabel framework for submodular function minimization and applications to parametric optimization. Discrete Appl. Math., 131: 311-322, 2003.
7. J. Friedman, T. Hastie, H. Holfling, and R. Tibshirani. Pathwise coordinate optimization. Annals of statistics, 1(2): 302-332, 2007.
8. S. Fujishige. Lexicographically optimal base of a polymatroid with respect to a weight vector. Mathematics of Operations Research, 5: 186-196, 1980.
9. S. Fujishige. Submodular Functions and Optimization. Elsevier, 2nd edition, 2005.
10. S. Fujishige, T. Hayashi, and S. Isotani. The minimum-norm-point algorithm applied to submodular function minimization and linear programming. Technical report, Research Institute for Mathematical Sciences Preprint RIMS-1571, Kyoto University, Kyoto, Japan, 2006.
11. G. Gallo, M. D. Grigoriadis, and R. E. Tarjan. A fast parametric maximum flow algorithm and applications. SIAM Journal on Computing, 18: 30-55, 1989.
12. A. V. Goldberg and R. E. Tarjan. A new approach to the maximum flow problem. Journal of the ACM, 35: 921-940, 1988.
13. S. Iwata and K. Nagano. Submodular function minimization under covering constraints. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), pages 671-680, 2009.
14. S. Jegelka, H. Lin, and J. Bilmes. On fast approximate submodular minimization. In Advances in Neural Information Processing Systems 24 (NIPS 2011), pages 460-468, 2011.
15. Pushmeet Kohli, Lubor Ladicky, and Philip H.S. Torr. Robust higher order potentials for enforcing label consistency. International Journal of Computer Vision, 82: 302-324, 2009.
16. V. Kolmogorov. A faster algorithm for computing the principal sequence of partitions ofa graph. Algorithmica, 56: 394-412, 2010.
17. L. Lovász. Submodular functions and convexity. In A. Bachem, M. Grötschel, and B. Korte, editors, Mathematical Programming - The State of the Art, pages 235-257. Springer-Verlag, 1983.
18. J. Mairal, F. Bach, J. Ponce, G. Sapiro, R. Jenatton, and G. Obozinski. SPArse Modeling Software. http://spams-devel.gforge.inria.fr/.
19. J. Mairal, R. Jenatton, G. Obozinski, and F. Bach. Convex and network flow optimization for structured sparsity. Journal of Machine Learning Research, 12: 2681-2720, 2011.
20. N. Megiddo. Optimal flows in networks with multiple sources and sinks. Mathematical Programming, 7: 97-107, 1974.
21. K. Nagano. A faster parametric submodular function minimization algorithm and applications. Technical report, METR 2007-43, University of Tokyo, Tokyo, Japan, 2007.
22. K. Nagano and K. Aihara. Equivalence of convex minimization problems over base polytopes. Japan journal of industrial and applied mathematics, 29: 519-534, 2012.
23. K. Nagano, Y. Kawahara, and K. Aihara. Sizeconstrained submodular minimization through minimum norm base. In Proceedings of the 28th International Conference on Machine Learning (ICML 2011), pages 977-984, 2011.
24. K. Nagano, Y. Kawahara, and S. Iwata. Minimum average cost clustering. In Advances in Neural Information Processing Systems 23 (NIPS 2010), pages 1759-1767, 2010.
25. M. Narasimhan, N. Jojic, and J. Bilmes. Q-clustering. In Advances in Neural Information Processing Systems 18 (NIPS 2005), pages 979-986, 2005.
26. Yu. Nesterov. Smooth minimization of non-smooth functions. Mathematical Programming, 103: 127-152, 2005.
27. J. B. Orlin. A faster strongly polynomial time algorithm for submodular function minimization. Mathematical Programming, 118: 237-251, 2009.
28. J. B. Orlin. Max flows in O(nm) time or less. In Proceedings of the 45th ACM Symposium on the Theory of Computing (STOC 2013), 2013. To appear.
29. M. Queyranne. Minimizing symmetric submodular functions. Mathematical Programming, 82: 3-12, 1998.
30. A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer-Verlag, 2003.
31. P. Stobbe and A. Krause. Efficient minimization of decomposable submodular functions. In Advances in Neural Information Processing Systems 23 (NIPS 2010), pages 2208-2216, 2010.