Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Atkinson AC, Donev AN, Tobias RD (2007) Optimum experimental designs, with SAS. Oxford University Press, New York
Cook D, Fedorov V (1995) Constrained optimization of experimental design. Statistics 26:129–178
Fellman J (1974) On the allocation of linear observations (Thesis). Comment Phys Math 44(2):27–78
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
Patan M (2012) Distributed scheduling of sensor networks for identification of spatio-temporal processes. Int J Appl Math Comput Sci 22(2):299–311
Patriksson M (2001) Simplicial decomposition algorithms. In: Floudas CA, Pardalos PM (eds) Encyclopedia of optimization, vol 5. Kluwer, Dordrecht, pp 205–212
Pázman A (1986) Foundations of optimum experimental design. Reidel, Dordrecht
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
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 Unpublished Ph.D. Thesis, University of Glasgow.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 http://theses.gla.ac.uk/1088/1/1981torsneyphd.pdf
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
Uciński D (2005) Optimal measurement methods for distributed-parameter system identification. CRC Press, Boca Raton
Uciński D (2012) Sensor network scheduling for identification of spatially distributed processes. Int J Appl Math Comput Sci 22(1):25–40
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Uciński, D. (2015). An Algorithm for Construction of Constrained D-Optimum Designs. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_51
Download citation
DOI: https://doi.org/10.1007/978-3-319-13881-7_51
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13880-0
Online ISBN: 978-3-319-13881-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)