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Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion Cover

Construction of constrained experimental designs on finite spaces for a modified Ek-optimality criterion

Open Access
|Dec 2020

References

  1. Atkinson, A.C., Donev, A.N. and Tobias, R.D. (2007). Optimum Experimental Designs, with SAS, Oxford University Press, Oxford.
  2. Beddiaf, S., Autrique, L., Perez, L. and Jolly, J.-C. (2016). Heating source localization in a reduced time, International Journal of Applied Mathematics and Computer Science26(3): 623–640, DOI: 10.1515/amcs-2016-0043.10.1515/amcs-2016-0043
  3. Bernstein, D.S. (2005). Matrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.
  4. Bertsekas, D.P. (1999). Nonlinear Programming, 2nd Edn, Optimization and Computation Series, Athena Scientific, Belmont, MA.
  5. Bertsekas, D.P. (2015). Convex Optimization Algorithms, Athena Scientific, Belmont, MA.
  6. Bertsekas, D. and Yu, H. (2011). A unifying polyhedral approximation framework for convex optimization, SIAM Journal on Optimization21(1): 333–360.10.1137/090772204
  7. Böhning, D. (1986). A vertex-exchange-method in D-optimal design theory, Metrika33(12): 337–347.10.1007/BF01894766
  8. Botkin, N.D. and Stoer, J. (2005). Minimization of convex functions on the convex hull of a point set, Mathematical Methods of Operations Research62(2): 167–18.10.1007/s00186-005-0018-4
  9. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press, Cambridge.10.1017/CBO9780511804441
  10. Burclová, K. and Pázman, A. (2016). Optimal design of experiments via linear programming, Statistical Papers57(4): 893–910.10.1007/s00362-016-0782-7
  11. Chepuri, S.P. and Leus, G. (2015). Sparsity-promoting sensor selection for non-linear measurement models, IEEE Transactions on Signal Processing63(3): 684–698.10.1109/TSP.2014.2379662
  12. Coll, C. and Sánchez, E. (2019). Parameter identification and estimation for stage-structured population models, International Journal of Applied Mathematics and Computer Science29(2): 327–336, DOI: 10.2478/amcs-2019-0024.10.2478/amcs-2019-0024
  13. Cook, D. and Fedorov, V. (1995). Constrained optimization of experimental design, Statistics26: 129–178.10.1080/02331889508802474
  14. Djelassi, H., Glass, M. and Mitsos, A. (2019). Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints, Journal of Global Optimization75(2): 341–392.10.1007/s10898-019-00764-3
  15. Duarte, B.P.M., Granjo, J.F.O. and Wong, W.K. (2020). Optimal exact designs of experiments via mixed integer nonlinear programming, Statistics and Computing30(1): 93–112.10.1007/s11222-019-09867-z
  16. Duarte, B.P.M. and Wong, W.K. (2014). A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models, Statistics and Computing24(6): 1063–1080.10.1007/s11222-013-9420-6
  17. Esteban-Bravo, M., Leszkiewicz, A. and Vidal-Sanz, J.M. (2017). Exact optimal experimental designs with constraints, Statistics and Computing27(3): 845–863.10.1007/s11222-016-9658-x
  18. Fedorov, V.V. (1989). Optimal design with bounded density: Optimization algorithms of the exchange type, Journal of Statistical Planning and Inference22: 1–13.10.1016/0378-3758(89)90060-8
  19. Fedorov, V.V. and Leonov, S.L. (2014). Optimal Design for Nonlinear Response Models, CRC Press, Boca Raton, FL.10.1201/b15054
  20. Harman, R. (2004). Minimal efficiency of designs under the class of orthogonally invariant information criteria, Metrika60(2): 137–153.10.1007/s001840300301
  21. Harman, R. and Benková, E. (2017). Barycentric algorithm for computing d-optimal size- and cost-constrained designs of experiments, Metrika80(2): 201–225.10.1007/s00184-016-0599-3
  22. Harman, R., Filová, L. and Richtárik, P. (2020). A randomized exchange algorithm for computing optimal approximate designs of experiments, Journal of the American Statistical Association115(529): 348–361.10.1080/01621459.2018.1546588
  23. Harman, R. and Pronzato, L. (2007). Improvements on removing nonoptimal support points in d-optimum design algorithms, Statistics & Probability Letters77(1): 90–94.10.1016/j.spl.2006.05.014
  24. Harville, D.A. (1997). Matrix Algebra From a Statistician’s Perspective, Springer-Verlag, New York, NY.10.1007/b98818
  25. Herzog, R., Riedel, I. and Uciński, D. (2018). Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics, Optimization and Engineering19(3): 591–627.10.1007/s11081-018-9391-8
  26. Hettich, R. and Kortanek, K.O. (1993). Semi-infinite programming: Theory, methods and applications, SIAM Review35(3): 380–429.10.1137/1035089
  27. Jacobson, M.Z. (1999). Fundamentals of Atmospheric Modeling, Cambridge University Press, Cambridge.
  28. Joshi, S. and Boyd, S. (2009). Sensor selection via convex optimization, IEEE Transactions on Signal Processing57(2): 451–462.10.1109/TSP.2008.2007095
  29. Katoh, N. (2001). Combinatorial optimization algorithms in resource allocation problems, in C.A. Floudas and P.M. Pardalos (Eds), Encyclopedia of Optimization, Vol. 1, Kluwer Academic Publishers, Dordrecht, pp. 259–264.10.1007/0-306-48332-7_56
  30. Khapalov, A.Y. (2010). Source localization and sensor placement in environmental monitoring, International Journal of Applied Mathematics and Computer Science20(3): 445–458, DOI: 10.2478/v10006-010-0033-3.10.2478/v10006-010-0033-3
  31. Langtangen, H.P. and Logg, A. (2016). Solving PDEs in Python. The FEniCS Tutorial I, Springer-Verlag, Cham.10.1007/978-3-319-52462-7
  32. Larsson, T., Migdalas, A. and Patriksson, M. (2015). A generic column generation principle: Derivation and convergence analysis, Operational Research15(2): 163–198.10.1007/s12351-015-0171-3
  33. Larsson, T., Patriksson, M. and Strömberg, A. (1998). Ergodic convergence in subgradient optimization, Optimization Methods and Software9(1–3): 93–120.10.1080/10556789808805688
  34. Lu, Z. and Pong, T.K. (2013). Computing optimal experimental designs via interior point method, SIAM Journal on Matrix Analysis and Applications34(4): 1556–1580.10.1137/120895093
  35. Maculan, N., Santiago, C.P., Macambira, E.M. and Jardim, M.H.C. (2003). An O(n) algorithm for projecting a vector on the intersection of a hyperplane and a box in ℝn, Journal of Optimization Theory and Applications117(3): 553–574.10.1023/A:1023997605430
  36. Marshall, A.W., Olkin, I. and Arnold, B.C. (2011). Inequalities: Theory of Majorization and Its Applications, 2nd Edn, Springer-Verlag, New York, NY.10.1007/978-0-387-68276-1
  37. Melas, V. (2006). Functional Approach to Optimal Experimental Design, Springer-Verlag, New York, NY.
  38. Patan, M. and Kowalów, D. (2018). Distributed scheduling of measurements in a sensor network for parameter estimation of spatio-temporal systems, International Journal of Applied Mathematics and Computer Science28(1): 39–54, DOI: 10.2478/amcs-2018-0003.10.2478/amcs-2018-0003
  39. Patan, M. and Uciński, D. (2008). Configuring a sensor network for fault detection in distributed parameter systems, International Journal of Applied Mathematics and Computer Science18(4): 513–524, DOI: 10.2478/v10006-008-0045-4.10.2478/v10006-008-0045-4
  40. Patan, M. and Uciński, D. (2019). Generalized simplicial decomposition for optimal sensor selection in parameter estimation of spatiotemporal processes, 2019 American Control Conference (ACC), Philadelphia, PA, USA, pp. 2546–2551.
  41. Patriksson, M. (2001). Simplicial decomposition algorithms, in C.A. Floudas and P.M. Pardalos (Eds), Encyclopedia of Optimization, Vol. 5, Kluwer Academic Publishers, Dordrecht, pp. 205–212.10.1007/0-306-48332-7_468
  42. Pázman, A. (1986). Foundations of Optimum Experimental Design, Mathematics and Its Applications, D. Reidel Publishing Company, Dordrecht.
  43. Polak, E. (1987). On the mathematical foundations of nondifferentiable optimization in engineering design, SIAM Review29(1): 21–89.10.1137/1029002
  44. Polak, E. (1997). Optimization. Algorithms and Consistent Approximations, Applied Mathematical Sciences, Springer-Verlag, New York, NY.10.1007/978-1-4612-0663-7
  45. Pronzato, L. (2003). Removing non-optimal support points in D-optimum design algorithms, Statistics & Probability Letters63: 223–228.10.1016/S0167-7152(03)00081-6
  46. Pronzato, L. and Pàzman, A. (2013). Design of Experiments in Nonlinear Models. Asymptotic Normality, Optimality Criteria and Small-Sample Properties, Springer-Verlag, New York, NY.10.1007/978-1-4614-6363-4
  47. Pronzato, L. and Zhigljavsky, A.A. (2014). Algorithmic construction of optimal designs on compact sets for concave and differentiable criteria, Journal of Statistical Planning and Inference154: 141–155.10.1016/j.jspi.2014.04.005
  48. Pukelsheim, F. (1993). Optimal Design of Experiments, Probability and Mathematical Statistics, John Wiley & Sons, New York, NY.
  49. Reemtsen, R. and Görner, S. (1998). Numerical methods for semi-infinite programming: A survey, in R. Reemtsen and J.-J. Rückmann (Eds), Semi-Infinite Programming,Kluwer Academic Publishers, Boston, MA, pp. 195–275.10.1007/978-1-4757-2868-2_7
  50. Sagnol, G. (2011). Computing optimal designs of multiresponse experiments reduces to second-order cone programming, Journal of Statistical Planning and Inference141(5): 1684–1708.10.1016/j.jspi.2010.11.031
  51. Sagnol, G. and Harman, R. (2015). Computing exact D-optimal designs by mixed integer second-order cone programming, The Annals of Statistics43(5): 2198–2224.10.1214/15-AOS1339
  52. Sahm, M. and Schwabe, R. (2001). A note on optimal bounded designs, in A. Atkinson et al. (Eds), Optimum Design 2000, Kluwer Academic Publishers, Dordrecht, Chapter 13, pp. 131–140.10.1007/978-1-4757-3419-5_13
  53. Seber, G.A.F. and Wild, C.J. (1989). Nonlinear Regression, John Wiley & Sons, New York, NY.10.1002/0471725315
  54. Shimizu, K. and Aiyoshi, E. (1980). Necessary conditions for min-max problems and algorithms by a relaxation procedure, IEEE Transactions on Automatic ControlAC-25(1): 62–66.10.1109/TAC.1980.1102226
  55. Silvey, S.D., Titterington, D.M. and Torsney, B. (1978). An algorithm for optimal designs on a finite design space, Communications in Statistics—Theory and Methods14: 1379–1389.10.1080/03610927808827719
  56. Torsney, B. and Mandal, S. (2001). Construction of constrained optimal designs, in A. Atkinson et al. (Eds), Optimum Design 2000, Kluwer Academic Publishers, Dordrecht, Chapter 14, pp. 141–152.10.1007/978-1-4757-3419-5_14
  57. Uciński, D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL.10.1201/9780203026786
  58. Uciński, D. (2012). Sensor network scheduling for identification of spatially distributed processes, International Journal of Applied Mathematics and Computer Science22(1): 25–40, DOI: 10.2478/v10006-012-0002-0.10.2478/v10006-012-0002-0
  59. Uciński, D. (2015). An algorithm for construction of constrained D-optimum designs, in A. Steland et al. (Eds), Stochastic Models, Statistics and Their Applications, Springer Proceedings in Mathematics & Statistics, Springer-Verlag, Cham, pp. 461–468.10.1007/978-3-319-13881-7_51
  60. Uciński, D. (2020). D-optimal sensor selection in the presence of correlated measurement noise, Measurement164: 107873.10.1016/j.measurement.2020.107873
  61. Uciński, D. and Patan, M. (2007). D-optimal design of a monitoring network for parameter estimation of distributed systems, Journal of Global Optimization39(2): 291–322.10.1007/s10898-007-9139-z
  62. Wu, C.-F. (1978). Some algorithmic aspects of the theory of optimal designs, The Annals of Statistics6(6): 1286–1301.10.1214/aos/1176344374
  63. Yu, Y. (2010). Monotonic convergence of a general algorithm for computing optimal designs, The Annals of Statistics38(3): 1593–1606.10.1214/09-AOS761
  64. Yu, Y. (2011). D-optimal designs via a cocktail algorithm, Statistics and Computing21(3): 475–481.10.1007/s11222-010-9183-2
  65. Zarrop, M.B. and Goodwin, G.C. (1975). Comments on “Optimal inputs for system identification”, IEEE Transactions on Automatic ControlAC-20(2): 299–300.10.1109/TAC.1975.1100891
  66. Zhang, L., Wu, S.-Y. and López, M.A. (2010). A new exchange method for convex semi-infinite programming, SIAM Journal on Optimization20(6): 2959–2977.10.1137/090767133
DOI: https://doi.org/10.34768/amcs-2020-0049 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 659 - 677
Submitted on: May 23, 2020
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Accepted on: Oct 13, 2020
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Published on: Dec 31, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2020 Dariusz Uciński, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.