An Algorithm for Construction of Constrained D-Optimum Designs

  • Dariusz UcińskiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 122)


A computational algorithm is proposed for determinant maximization over the set of all convex combinations of a finite number of nonnegative definite matrices subject to additional box constraints on the weights of those combinations. The underlying idea is to apply a simplicial decomposition algorithm in which the restricted master problem reduces to an uncomplicated multiplicative weight optimization algorithm.


Fisher Information Matrix Restricted Master Problem Optimum Experimental Design Simplicial Decomposition Multiplicative Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Atkinson AC, Donev AN, Tobias RD (2007) Optimum experimental designs, with SAS. Oxford University Press, New York Google Scholar
  2. 2.
    Cook D, Fedorov V (1995) Constrained optimization of experimental design. Statistics 26:129–178 MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fellman J (1974) On the allocation of linear observations (Thesis). Comment Phys Math 44(2):27–78 MathSciNetGoogle Scholar
  4. 4.
    Harman R, Trnovská M (2009) Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices. Math Slovaca 59:693–704 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Patan M (2012) Distributed scheduling of sensor networks for identification of spatio-temporal processes. Int J Appl Math Comput Sci 22(2):299–311 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Patriksson M (2001) Simplicial decomposition algorithms. In: Floudas CA, Pardalos PM (eds) Encyclopedia of optimization, vol 5. Kluwer, Dordrecht, pp 205–212 Google Scholar
  7. 7.
    Pázman A (1986) Foundations of optimum experimental design. Reidel, Dordrecht Google Scholar
  8. 8.
    Sahm M, Schwabe R (2001) A note on optimal bounded designs. In: Atkinson A, Bogacka B, Zhigljavsky A (eds) Optimum design 2000. Kluwer, Dordrecht, pp 131–140 CrossRefGoogle Scholar
  9. 9.
    Torsney B (1981) Algorithms for a constrained optimisation problem with applications in statistics and optimum design. Unpublished Ph.D. Thesis, University of Glasgow. Available at
  10. 10.
    Torsney B, Mandal S (2004) Multiplicative algorithms for constructing optimizing distributions: further developments. In: Di Bucchianico A, Läuter H, Wynn HP (eds) mODa 7. Proc 7th int workshop on model-oriented data analysis. Physica-Verlag, Heidelberg, pp 163–171 Google Scholar
  11. 11.
    Uciński D (2005) Optimal measurement methods for distributed-parameter system identification. CRC Press, Boca Raton Google Scholar
  12. 12.
    Uciński D (2012) Sensor network scheduling for identification of spatially distributed processes. Int J Appl Math Comput Sci 22(1):25–40 MathSciNetGoogle Scholar
  13. 13.
    Uciński D, Patan M (2007) D-optimal design of a monitoring network for parameter estimation of distributed systems. J Glob Optim 39(2):291–322 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringUniversity of Zielona GóraZielona GóraPoland

Personalised recommendations