The geometry of logconcave functions and sampling algorithms

Random Structures and Algorithms

Volumn 30, Issue 3, 2007, Pages 307-358

  Lovász, László ^a,c   Vempala, Santosh ^b  

^a MICROSOFT RESEARCH   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Isaac Newton Institute   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247517393     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20135     Document Type: Article

References (24)

1. D. Applegate and R. Kannan, Sampling and integration of near log-concave functions, Proc 23rd ACM STOC, 1990, pp. 156-163.
2. D. Bertsimas and S. Vempala, Solving convex programs by random walks, J ACM 51 (4) (2004), 540-556.
3. J. Bourgain, "Random points in isotropic convex sets," Convex geometric analysis, Berkeley, CA, 1996, Math Sci Res Inst Publ, 34, Cambridge Univ. Press, 1999, pp. 53-58.
4. A. Dinghas, Über eine Klasse superadditiver Mengenfunktionale von Brunn-Minkowski-Lusternik-schem Typus, Math Zeitschr 68 (1957), 111-125.
5. M. Dyer, A. Frieze, and R. Kannan, A random polynomial time algorithm for estimating volumes of convex bodies, Proc 21st Annu ACM Symp Theory Comput, 1989, pp. 375-381.
6. M. Dyer, A. Frieze, and L. Stougie, Talk at the Math. Prog. Symp., Ann Arbor, Michigan, 1994.
7. A. Frieze, R. Kannan, and N. Polson, Sampling from log-concave distributions, Ann Appl Probab 4 (1994), 812-837; Correction: Sampling from log-concave distributions, ibid. 4 (1994), 1255.
8. A. Frieze and R. Kannan, Log-Sobolev inequalities and sampling from log-concave distributions, Ann Appl Probab 9 (1999), 14-26.
9. M. Jerrum and A. Sinclair, Approximating the permanent, SIAM J Comput 18 (1989), 1149-1178.
10. A. Kalai and S. Vempala, Efficient algorithms for universal portfolios, J Mach Learn Res 3 (2002), 423-440.
11. R. Kannan and L. Lovász, "A logarithmic Cheeger inequality and mixing in random walks," Proc. 31st Annual ACM STOC, 1999, pp. 282-287.
12. 5) volume algorithm for convex bodies, Random Struct Algor 11 (1997), 1-50.
13. R. Kannan, L. Lovász, and M. Simonovits, Isoperimetric problems for convex bodies and a localization lemma, J Discr Comput Geom 13 (1995), 541-559.
14. L. Lovász, How to compute the volume?, Jber d Dt Math-Verein Jubiläumstagung 1990, B.G. Teubner, Stuttgart, 1992, pp. 138-151.
15. L. Lovász, Hit-and-run mixes fast, Math Prog 86 (1998), 443-461.
16. L. Lovász and M. Simonovits, Random walks in a convex body and an improved volume algorithm, Random Struct Algor 4 (1993), 359-412.
17. L. Lovász and S. Vempala, Hit-and-run from a corner, SIAM J Comput 35(4) (2006), 985-1005.
18. L. Leindler, On a certain converse of Holder's Inequality II, Acta Sci Math Szeged 33 (1972), 217-223.
19. A. Prékopa, Logarithmic concave measures and functions, Acta Sci Math Szeged 34 (1973), 335-343.
20. A. Prékopa, On logarithmic concave measures with applications to stochasic programming, Acta Sci Math Szeged 32 (1973), 301-316.
21. A. Prékopa, Stochastic Programming, Akadémiai Kiadó, Budapest and Kluwer, Dordrecht, 1995.
22. M. Rudelson, Random vectors in the isotropic position, J Funct Anal 164 (1999), 60-72.
23. R. L. Smith, Efficient Monte-Carlo procedures for generating points uniformly distributed over bounded regions, Oper Res 32 (1984), 1296-1308.
24. Z. B. Zabinsky, R. L. Smith, J. F. McDonald, H. E. Romeijn, and D. E. Kaufman, Improving hit-and-run for global optimization, J Global Optim 3 (1993), 171-192.