A minimax theorem with applications to machine learning, signal processing, and finance

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2007, Pages 751-758

  Kim, Seung Jean ^a   Boyd, Stephen ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRIMINANT ANALYSIS; FINANCE; FUNCTIONS; GAME THEORY; LEARNING SYSTEMS; OPTIMIZATION; SIGNAL PROCESSING;

CONVEX OPTIMIZATION; FRACTIONAL FUNCTIONS; STATISTICAL MODELS;

THEOREM PROVING;

EID: 62749086414     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2007.4434853     Document Type: Conference Paper

References (28)

1. A. Ben-Tal and A. Nemirovski. Robust convex optimization. Mathematics of Operations Research, 23(4):769-805, 1998.
2. A. Ben-Tal and A. Nemirovski. Robust optimization: methodology and applications. Mathematical Programming Series B, 92(3):453-480, May 2002.
3. D. Bertsekas, A. Nedić, and A. Ozdaglar. Convex Analysis and Optimization. Athena Scientific, 2003.
4. D. Bertsimas and I. Popescu. Optimal inequalities in probability theory: A convex optimization approach. SIAM Journal on Optimization, 15(3):780-804, 2005.
5. J. Cochrane. Asset Pricing. Princeton University Press, NJ: Princeton, second edition, 2001.
6. L. El Ghaoui, M. Oks, and F. Oustry. Worst-case Value-At-Risk and robust portfolio optimization: A conic programming approach. Operations Research, 51(4):543-556, 2003.
7. D. Goldfarb and G. Iyengar. Robust portfolio selection problems. Mathematics of Operations Research, 28(1):1-38, 2003.
8. B. Halldórsson and R. Tütüncü. An interior-point method for a class of saddle point problems. Journal of Optimization Theory and Applications, 116(3):559-590, 2003.
9. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer Series in Statistics. Springer-Verlag, New York, 2001.
10. S. Kassam and T. Lim. Robust Wiener filters. Journal of Franklin Institute, 304:171-185, 1977.
11. S. Kassam, T. Lim, and L. Climini. Two dimensional filters for signal processing under modeling uncertainties. IEEE Transactions on Georscience Electronics, 18:331-336, 1980.
12. S. Kassam and V. Poor. Robust techniques for signal processing: A survey. Proceedings of IEEE, 73:433-481, 1985.
13. S.-J. Kim and S. Boyd. A minimax theorem with applications to machine learning, signal processing, and finance, 2006. Manuscript. Available from www.stanford.edu/~boyd/minimax.frac.html.
14. S.-J. Kim, A. Magnani, and S. Boyd. Robust Fisher discriminant analysis. In Advances in Neural Information Processing Systems, MIT Press, 2006.
15. S.-J. Kim, A. Magnani, A. Mutapcic, S. Boyd, and Z.-Q. Luo. Robust beamforming via worst-case SINR maximization, 2007. Accepted to IEEE Transactions on Signal Processing. Available from www.Stanford.edu/~boyd/ robust_bf.html.
16. M. Lobo and S. Boyd. The worst-case risk of a portfolio. Unpublished manuscript. Available from http://faculty.fuqua.duke.edu/%7Emlobo/bio/ researchfiles/rsk-bnd.pdf, 2000.
17. H. Markowitz. Portfolio selection. Journal of Finance, 7(1):77-91, 1952.
18. H. Markowitz. Portfolio Selection. J. Wiley & Sons, New York, 1959.
19. A. Mutapcic, S.-J. Kim, and S. Boyd. Array signal processing with robust rejection constraints via second-order cone programming. In Proceedings of the 40th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, October 2006.
20. M. Pinar and R. Tütüncü. Robust profit opportunities in risky financial portfolios. Operations Research Letters, 33(4):331-340, 2005.
21. H. Poor. Robust matched filters. IEEE Transactions on Information Theory, 29(5):677-687, 1983.
22. W. Sharpe. The Sharpe ratio. Journal of Portfolio Management, 21(1):49-58, 1994.
23. M. Sion. On general minimax theorems. Pacific Journal of Mathematics, 8:171-176, 1958.
24. H. Van Trees. Detection, Estimation, and Modulation Theory, Part I. Wiley-Interscience, 2001.
25. L. Vandenberghe, S. Boyd, and K. Comanor. Generalized Chebyshev bounds via semidefinite programming. SIAM Review, 49(1):52-64, 2007.
26. S. Verdú and H. Poor. Minimax robust discrete-time matched filters. IEEE Transactions on Communications, 31(2):208-215, 1983.
27. S. Verdú and H. Poor. Signal selection for robust matched filtering. IEEE Transactions on Communications, 31(5):667-670, 1983.
28. S. Verdú and H. Poor. On minimax robustness: A general approach and applications. IEEE Transactions on Information Theory, 30(2):328-340, 1984.