Maximizing a class of submodular utility functions

Mathematical Programming

Volumn 128, Issue 1-2, 2011, Pages 149-169

  Ahmed, Shabbir ^a   Atamtürk, Alper ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b DEPARTMENT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH   (United States)

Author keywords

Combinatorial auctions; Competitive facility location; Expected utility maximization; Polyhedra; Submodular function maximization

Indexed keywords

COMBINATORIAL AUCTION; COMPETITIVE FACILITY LOCATION; EXPECTED UTILITY; POLYHEDRA; SUBMODULAR FUNCTIONS;

CARBON FIBER REINFORCED PLASTICS; COMBINATORIAL OPTIMIZATION; COMMERCE; OPTIMIZATION;

BUDGET CONTROL;

EID: 79957951066     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-009-0298-1     Document Type: Article

References (29)

1. R. Aboolian O. Berman D. Krass 2007 Competitive facility location model with concave demand Eur. J. Oper. Res. 181 598 619 2308701 1131.90027 10.1016/j.ejor.2005.10.075 (Pubitemid 46413589)
2. A. Atamtürk 2004 Sequence independent lifting for mixed-integer programming Oper. Res. 52 487 490 2066040 1165.90576 10.1287/opre.1030.0099 (Pubitemid 40000797)
3. E. Balas 1975 Facets of the knapsack polytope Math. Program. 8 146 164 437053 0316.90046 10.1007/BF01580440
4. O. Berman D. Krass 1998 Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities Locat. Sci. 6 41 65 10.1016/S0966-8349(98)00047-3
5. J.L. Corner P.D. Corner 1995 Characteristics of decisions in decision analysis practice J. Oper. Res. Soc. 46 304 314 0822.90087
6. Dobzinski, S.; Nisan, N.; Schapira, M.: Approximation algorithms for combinatorial auctions with complement-free bidders. In: STOC 2005 Proceedings of the 37th annual ACM symposium on theory of computing, pp. 610-618. ACM (2005) (Pubitemid 43098634)
7. Feige, U.: On maximizing welfare when utility functions are subadditive. In: STOC 2006 Proceedings of the thirty-eighth annual ACM symposium on theory of computing, pp. 41-50. ACM (2006) (Pubitemid 44306536)
8. Feige, U.; Mirrokni V.S.; Vondrák J.: Maximizing non-monotone submodular functions. In: FOCS 2007 Proceedings of the 48th annual IEEE symposium on foundations of computer science, pp. 461-471. IEEE (2007)
9. Garey M.R.; Johnson D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)
10. Z. Gu G.L. Nemhauser M.W.P. Savelsbergh 2000 Sequence independent lifting in mixed integer programming J. Comb. Optim. 4 109 129 1747826 0964.90030 10.1023/A:1009841107478
11. P.L. Hammer E.L. Johnson U.N. Peled 1975 Facets of regular 0-1 polytopes Math. Program. 8 179 206 384128 0314.90064 10.1007/BF01580442
12. Hille E.; Phillips R.S.: Functional Analysis and Semi-Groups. American Mathematical Society, Providence (1957)
13. D.L. Huff 1964 Defining and estimating a trade area J. Mark. 28 34 38 10.2307/1249154
14. T.D. Klastorin 1990 On a discrete nonlinear and nonseparable knapsack problem Oper. Res. Lett. 9 233 237 1071455 0708.90079 10.1016/0167-6377(90) 90067-F
15. H. Lee G.L. Nemhauser Y. Wang 1996 Maximizing a submodular function by integer programming: polyhedral results for the quadratic case Eur. J. Oper. Res. 94 154 166 0918.90108 10.1016/0377-2217(95)00205-7 (Pubitemid 126390437)
16. Lehmann, B. Lehmann, D.; Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: EC '01 Proceedings of the 3rd ACM conference on electronic Commerce, pp. 18-28. ACM (2001)
17. B. Lehmann D. Lehmann N. Nisan 2006 Combinatorial auctions with decreasing marginal utilities Games Econ. Behav. 55 270 296 2221812 1125.91043 10.1016/j.geb.2005.02.006 (Pubitemid 43585597)
18. H. Marchand L.A. Wolsey 1999 The 0-1 knapsack problem with a single continuous variable Math. Program. 85 15 33 1689362 0956.90021 10.1007/s101070050044
19. A. Mehrez Z. Sinuany-Stern 1983 Resource allocation to interrelated risky projects using a multiattribute utility function Manag. Sci. 29 439 490 10.1287/mnsc.29.4.430
20. G.L. Nemhauser L.A. Wolsey 1978 Best algorithms for approximating the maximum of a submodular function Math. Oper. Res. 3 177 188 506656 0395.90072 10.1287/moor.3.3.177
21. Nemhauser G.L.; Wolsey L.A.: Integer and Combinatorial Optimization. Wiley, New York (1988)
22. G.L. Nemhauser L.A. Wolsey M.L. Fisher 1978 An analysis of approximations for maximizing submodular set functions-I Math. Program. 14 265 294 503866 0374.90045 10.1007/BF01588971
23. P.J.H. Schoemaker 1982 The expected utility model: its variants, purposes, evidence and limitations J. Econ. Lit. 20 529 563
24. von Neumann J.; Morgenstern O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1947)
25. Vondrak, J.: Optimal approximation for the submodular welfare problem in the value oracle model. In: STOC 2008 Proceedings of the fourth annual ACM symposium on theory of computing, pp. 67-74. ACM (2008)
26. H.M. Weingartner 1966 Capital budgeting of interrelated projects: survey and synthesis Manag. Sci. 12 485 516 10.1287/mnsc.12.7.485
27. L.A. Wolsey 1975 Faces for linear inequality in 0-1 variables Math. Program. 8 165 178 373604 0314.90063 10.1007/BF01580441
28. L.A. Wolsey 1977 Valid inequalities and superadditivity for 0/1 integer programs Math. Oper. Res. 2 66 77 503753 0402.90066 10.1287/moor.2.1.66
29. L.A. Wolsey 1988 Submodularity and valid inequalities in capacitated fixed charge networks Oper. Res. Lett. 8 119 124 1007266 10.1016/0167-6377(89) 90036-9