On convex minimization over base polytopes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4513 LNCS, Issue , 2007, Pages 252-266

  Nagano, Kiyohito ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Convex optimization; Submodular functions

Indexed keywords

ALGORITHMS; OPTIMIZATION; PARAMETER ESTIMATION; PROBLEM SOLVING;

CONVEX OPTIMIZATION PROBLEMS; DECOMPOSITION ALGORITHMS; POLYMATROIDS; SUBMODULAR FUNCTIONS; SUBMODULAR UTILITY ALLOCATION MARKETS;

INTEGER PROGRAMMING;

EID: 38049012815     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-72792-7_20     Document Type: Conference Paper

References (23)

1. R. E. Bixby, W. H. Cunningham and D. M. Topkis: The partial order of a polymatroid extreme point. Mathematics of Operations Research, 10 (1985), pp. 367-378.
2. F. A. Chudak and K. Nagano: Efficient solutions to relaxations of combinatorial problems with submodular penalties via the Lovász extension and non-smooth convex optimization. Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (2007), pp. 79-88.
3. B. Dutta: The egalitarian solution and reduced game properties in convex games. International Journal of Game Theory, 19 (1990), pp. 153-169.
4. B. Dutta and D. Ray: A Concept of egalitarianism under participation constraints. Econometrica, 57 (1989), pp. 615-635.
5. J. Edmonds: Submodular functions, matroids, and certain polyhedra. In R. Guy, H. Hanai, N. Sauer, and J. Schönheim, editors, Combinatorial Structures and Their Applications, Gordon and Breach, New York, 1970, pp. 69-87.
6. L. Fleischer and S. Iwata: A push-relabel framework for submodular function minimization and applications to parametric optimization. Discrete Applied Mathematics, 131 (2003), pp. 311-322.
7. S. Fujishige: Lexicographically optimal base of a polymatroid with respect to a weight vector. Mathematics of Operations Research, 5 (1980), pp. 186-196.
8. S. Fujishige: Submodular systems and related topics. Mathematical Programming Study, 22 (1984), pp. 113-131.
9. S. Fujishige: Submodular Functions and Optimization (Second Edition). Elsevier, Amsterdam, 2005.
10. G. Gallo, M. D. Grigoriadis and R. E. Tarjan: A fast parametric maximum flow algorithm and applications. SIAM Journal on Computing, 18 (1989), pp. 30-55.
11. H. Groenevelt: Two algorithms for maximizing a separable concave function over a polymatroid feasible region. European Journal of Operational Research, 54 (1991), pp. 227-236.
12. A. Hayrapetyan, C. Swamy and É. Tardos: Network design for information networks. Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (2005), pp. 933-942.
13. D. S. Hochbaum: Lower and upper bounds for the allocation problem and other nonlinear optimization problems. Mathematics of Operations Research, 19 (1994), pp. 390-409.
14. S. Iwata: A faster scaling algorithm for minimizing submodular functions. SIAM Journal on Computing, 32(2003), pp. 833-840.
15. K. Jain and V. V. Vazirani: Eisenberg-Gale markets: algorithms and structural properties. Proceedings of the 39th ACM Symposium on Theory of Computing (2007), to appear.
16. F. Maruyama: A unified study on problems in information theory via polymatroids. Graduation Thesis, University of Tokyo, Japan, 1978. (In Japanese.)
17. S. T. McCormick: Submodular function minimization. In K. Aardal, G. L. Nemhauser, and R. Weismantel, editors, Discrete Optimization (Handbooks in Operations Research and Management Science 12), Elsevier, Amsterdam, 2005, Chapter 7, pp. 321-391.
18. N. Megiddo: Optimal flows in networks with multiple sources and sinks. Mathematical Programming, 7 (1974), pp. 97-107.
19. K. Murota: Note on the universal bases of a pair of polymatroids. Journal of Operations Research Society of Japan, 31 (1988), pp. 565-573.
20. K. Murota: Discrete Convex Analysis. SIAM, Philadelphia, 2003.
21. J. B. Orlin: A faster strongly polynomial time algorithm for submodular function minimization. Proceedings of the 12th IPCO Conference (2007). This proceedings.
22. A. Schrijver: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory (B), 80(2000), pp. 346-355.
23. Y. Sharma, C. Swamy and D. P. Williamson: Approximation algorithms for prize-collecting forest problems with submodular penalty functions. Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (2007), pp. 1275-1284.