Probabilities, intervals, what next? Optimization problems related to extension of interval computations to situations with partial information about probabilities

Journal of Global Optimization

Volumn 29, Issue 3, 2004, Pages 265-280

  Kreinovich, V ^a  

^a University of Texas at El Paso   (United States)

Author keywords

Interval computations; Optimization; Robust statistics

Indexed keywords

ALGORITHMS; DATABASE SYSTEMS; INVERSE PROBLEMS; PROBABILITY; PROBLEM SOLVING; STATISTICAL METHODS;

INTERVAL COMPUTATIONS; QUADRATIC TIME; ROBUST STATISTICS; STATISTICAL DATABASE;

OPTIMIZATION;

EID: 6944233967     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000044769.91651.87     Document Type: Conference Paper

References (17)

1. Ferson, S., Ginzburg, L., Kreinovich, V., Longpré L. and Aviles, M. (2002), Computing variance for interval data is NP-hard, ACM SIGACT News 33, 108-118.
2. Ferson, S., Ginzburg, L., Kreinovich, V. and Lopez, J. (2002), Absolute bounds on the mean of sum product, etc.: a probabilistic extension of interval arithmentic, Extended Abstracts of the 2002 SIAM Workshop on Validated Computing, Toronto, Canada, May 23-25, pp. 70-72.
3. Jaulin, L., Keiffer, M., Didrit, O. and Walter, E. (2001), Applied Interval Analysis, Springer-Verlag, Berlin.
4. Kearfott, R.B. (1996), Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht.
5. Kearfott, R.B. and Kreinovich, V. (1996), Applications of interval computations. In: Pardalos, P.M. and Hearn, D. (eds.), Applied Optimization, Vol. 3, Kluwer, Dordrecht.
6. Kreinovich, V. (2000), Beyond interval systems: What is feasible and what is algorithmically solvable? In: Pardalos, P.M. (ed.), Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, Kluwer, Dordrecht, pp. 364-379.
7. Kreinovich, V., Lakeyev, A., Rohn, J. and Kahl, P. (1997), Computational complexity and feasibility of data processing and interval computations. In: Pardalos, P.M. and Hearn, D. (eds.), Applied Optimization, Vol. 10, Kluwer, Dordrecht.
8. Kreinovich, V., Nguyen, H.T., Ferson, S. and Ginzburg, L. (2002), From computation with guaranteed intervals to computation with confidence intervals, Proc. 21st Int'l Conf. of North American Fuzzy Information Processing Society NAFIPS'2002, New Orleans, Louisiana, pp. 418-422.
9. Kuznetsov, V.P. (1991), Interval Statistical Models, Radio i Svyaz, Moscow (in Russian).
10. Moore, R.E. (1979), Methods and Applications of Interval Analysis, SIAM, Philadelphia.
11. Nivlet, P., Fournier, P. and Royer, J. (2001), A New Methodology to Account for Uncertainties in 4-D Seismic Interpretation, Proceedings of the 71st Annual International Meeting of the Society of Exploratory Geophysics SEG'2001, San Antonio, Texas, September 9-14, pp. 16441647.
12. Nivlet, P., Fournier, F. and Royer, J. (2001), Propagating Interval Uncertainties in Supervised Pattern Recognition for Reservoir Characterization, Proceedings of the 2001 Society of Exploratory Geophysics SPE'2001, New Orleans, Louisiana, September 30-October 3, paper SPE-71327.
13. Osegueda, R., Kreinovich, V., Potluri, L. and Aló, R. (2002), Non-Destructive Testing of Aerospace Structures: Granularity and Data Mining Approach, Proceedings of FUZZ-IEEE'2002, Honolulu, Hawaii, May 12-17, Vol. 1, pp. 685-689.
14. Rabinovich, S. (1993), Measurement Errors: Theory and Practice, American Institute of Physics, New York.
15. Rowe, N.C. (1988), Absolute bounds on the mean and standard deviation of transformed data for constant-sign-derivative transformations, SIAM Journal of Scientific Statistical Computing, 9, 1098-1113.
16. Vavasis, S.A. (1991), Nonlinear Optimization: Complexity Issues, Oxford University Press, N.Y.
17. Walley, P. (1991), Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, N.Y.