Abstract
The duality relations between the pseudometrics of conjugate cones are considered and the structure of a dominating cone is studied. The relation of the suggested constructions to the problems of controlling a motion and modelling economic dynamics is shown.
Similar content being viewed by others
REFERENCES
Propoi, A.I., On Constructing a Metric on a Dominating Cone, Avtom. Telemekh., 2004, no. 4, pp. 81–90.
Makarov, V.L. and Rubinov, A.M., Matematicheskaya teoriya ekonomicheskoi dinamiki i ravnovesiya (The Mathematical Theory of Economic Dynamics and Equilibrium), Moscow: Nauka, 1973.
Rockafellar, R.T., Convex Analysis, Princeton: Princeton Univ. Press, 1970.
Propoi, A.I., The Principle of Equivalence in Controlling a Motion. I, Avtom. Telemekh., 1999, no. 10. pp. 89–96.
Shephard, R.W., Theory of Cost and Production Functions, Princeton: Princeton Univ. Press, 1970.
Rubinov, A.M., Superlineinye mnogoznachnye otobrazheniya i ikh prilozheniya k ekonomiko-matematicheskim zadacham (Superlinear Many-Valued Mappings and Its Applications to Economical and Mathematical Problems), Leningrad: Nauka, 1980.
Farrel, M.J., The Measurement of Productive Efficiency, J. Royal Statist. Soc., 1957, Series A (general), part III, pp. 253–281.
Charnes, A., Cooper, W.W., and Rhodes, E., Measuring the Efficiency of Decision Making Units, EJOR, 1978, no. 2, pp. 429–444.
Propoi, A.I., The Principle of Equivalence in Controlling a Motion. II, Avtom. Telemekh., 1999, no. 12. pp. 57–66.
Propoi, A.I., The Structure of Linear Controlling Systems, in Dynamics of Non-homogeneous Syst., Moscow: Inst. Sist. Analiz., 2002.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Propoi, A.I. On Constructing a Metric on a Dominating Cone. II. Automation and Remote Control 65, 733–740 (2004). https://doi.org/10.1023/B:AURC.0000028321.05170.35
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000028321.05170.35