Submodularity and randomized rounding techniques for optimal experimental design

Electronic Notes in Discrete Mathematics

Volumn 36, Issue C, 2010, Pages 679-686

  Bouhtou, Mustapha ^b   Gaubert, Stéphane ^a   Sagnol, Guillaume ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b ORANGE LABS   (France)

Author keywords

D optimality; Discrete optimization; Kiefer's p criterion; Optimal design of experiments; Polynomial time approximability

Indexed keywords

EID: 77954898336     PISSN: 15710653     EISSN: 15710653     Source Type: Journal    
DOI: 10.1016/j.endm.2010.05.086     Document Type: Article

References (16)

1. Ageev A.A., Sviridenko M.I. Pipage rounding: a new method of constructing algorithms with proven performance guarantee. Journal of Combinatorial Optimization 2004, 8.
2. Atwood C.L. Sequences converging to D-optimal designs of experiments. Annal of statistics 1973, 1:342-352.
3. Branderhorst M., Walmsley I., Kosut R., Rabitz H. Optimal experiment design for quantum state tomography of a molecular vibrational mode. Journal of Physics B: Atomic Molecular and Optical Physics 2008, 41. 074004.
4. G. Calinescu, C. Chekuri, M. Pál, and J. Vondrák. Maximizing a submodular set function subject to a matroid constraint. In Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization, IPCO, volume 4513, pages 182-196, 2007.
5. Dette H., Pepelyshev A., Zhigljavsky A. Improving updating rules in multiplicative algorithms for computing D-optimal designs. Computational Statistics & Data Analysis 2008, 53(2):312-320.
6. Fedorov V.V. Theory of optimal experiments 1972, Academic Press, New York, Translated and edited by W. J. Studden and E. M. Klimko.
7. Kiefer J. Optimal design: Variation in structure and performance under change of criterion. Biometrika 1975, 62(2):277-288.
8. A. Kulik, H. Shachnai, and T. Tamir. Maximizing submodular set functions subject to multiple linear constraints. In SODA '09: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 545-554, Philadelphia, PA, USA, 2009.
9. Nemhauser G.L., Wolsey L.A., Fisher M.L. An analysis of approximations for maximizing submodular set functions. Mathematical Programming 1978, 14:265-294.
10. Pukelsheim F. On linear regression designs which maximize information. Journal of statistical planning and inferrence 1980, 4:339-364.
11. Pukelsheim F. Optimal Design of Experiments 1993, Wiley.
12. G. Sagnol. Polynomial-time approximability results for combinatorial problems arising in optimal experimental design. Draft.
13. G. Sagnol, M. Bouhtou, and S. Gaubert. Optimization of network traffic measurement: a semidefinite programming approach. In Proceedings of the International Conference on Engineering Optimization (ENGOPT), Rio De Janeiro, Brazil, 2008. ISBN 978-85-7650-152-7.
14. H.H. Song, L. Qiu, and Y. Zhang. Netquest: A flexible framework for largescale network measurement. In ACM SIGMETRICS'06, St Malo, France, 2006.
15. Uciński D., Patan M. D-optimal design of a monitoring network for parameter estimation of distributed systems. Journal of Global Optimization 2007, 39(2):291-322.
16. Yu Y. Monotonic convergence of a general algorithm for computing optimal designs arxiv:/0905.2646v2.