Abstract
The problem of identifying points of two sets in \({\mathop{{\rm I}\mskip-2.0mu{\rm R}}^{n}}\) is considered. This problem is of interest by itself and has numerous practical applications. One of such applications—namely, to the ranking of parameters—is also mentioned in the paper. Two identification procedures are discussed: by means of a linear identifier (the separation method) and by means of isolation of one of the sets by an interval.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Demyanov V.F., Vasiliev L.V.: Nondifferentiable Optimization. Springer-Optimization Software, New York (1986)
Demyanov V.F., Rubinov A.M.: Constructive Nonsmooth Analysis. Verlag Peter Lang, Frankfurt a/M (1995)
Demyanova, V.V.: One-dimensional identification by the separation method // Vestnik of St.-Petersburg University; Ser. 10. Applied mathematics, informatics, control processes. No. 3, pp. 28–31 (2006)
Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Wilde D.J.: Optimum-Seeking Methods. Prentice-Hall, Englewood Cliffs (1963)
Zabotin, Y.I., Korablev, F.I., Khabibulin, R.F.: On minimizing quasiconvex functionals // Izvestiya Vuzov. Mathematics. No. 10, pp. 27–33 (1972)
Author information
Authors and Affiliations
Corresponding author
Additional information
The work was supported by the Russian Foundation for Fundamental Studies (RFFI) under Grant No. 06-01-00276.
Rights and permissions
About this article
Cite this article
Demyanova, V.V., Demyanov, V.F. One-dimensional identification problem and ranking parameters. J Glob Optim 48, 29–40 (2010). https://doi.org/10.1007/s10898-009-9509-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9509-9