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Autoregressive processes in optimization

Published online by Cambridge University Press:  14 July 2016

Tomáš Cipra
Tomáš Cipra*
Affiliation:
Charles University of Prague
*
∗Postal address: Department of Statistics, Charles University, Sokolovská 83, 186 00 Prague 8, Czechoslovakia.
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Abstract

Vector autoregressive processes of the first order are considered which are non-negative and optimize a linear objective function. These processes may be used in stochastic linear programming with a dynamic structure. By using Tweedie's results from the theory of Markov chains, conditions for geometric rates of convergence to stationarity (i.e. so-called geometric ergodicity) and for existence and geometric convergence of moments of these processes are obtained.

Keywords

GEOMETRIC ERGODICITYSTOCHASTIC PROGRAMMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 302 - 312
Copyright
Copyright © Applied Probability Trust 1988 

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References

Bubnik, J. and Keder, J. (1983) Prognostic and Signal Systems of Air Protection in North Bohemia Brown Coal Basin . Research Reports of Czech Hydrometeorologic Institute 28 (in Czech).Google Scholar
Cipra, T. (1986a) Confidence regions for linear programs with random coefficients. Working Paper WP-86–20, International Institute for Applied Systems Analysis, Laxenburg.Google Scholar
Cipra, T. (1986b) Time series in linear programs with random right-hand sides. Working Paper WP-86–21, International Institute for Applied Systems Analysis, Laxenburg.Google Scholar
Cipra, T. (1987) Prediction in stochastic linear programming. Kybernetika 23, 214–226.Google Scholar
Faddeev, D. K. and Faddeeva, V. N. (1960) Numerical Methods of Linear Algebra. Fizmatgiz, Moscow (in Russian).Google Scholar
Feigin, P. D. and Tweedie, R. L. (1985) Random coefficient autoregressive processes: A Markov chain analysis of stationarity and finiteness of moments. J. Time Series Anal. 6, 1–14.Google Scholar
Kall, P. (1976) Stochastic Linear Programming. Springer-Verlag, Berlin.Google Scholar
Lankaster, P. (1969) Theory of Matrices. Academic Press, New York.Google Scholar
Petruccelli, J. D. and Woolford, S. W. (1984) A threshold AR(1) model. J. Appl. Prob. 21, 270–286.Google Scholar
Theil, H. (1964) Optimal Decision Rules for Government and Industry. North-Holland, Amsterdam.Google Scholar
Tweedie, R. L. (1983a) Criteria for rates of convergence of Markov chains with application to queueing and storage theory. In Probability, Statistics and Analysis , ed. Kingman, J. F. C. and Reuter, G. E. H. Cambridge University Press, Cambridge.Google Scholar
Tweedie, R. L. (1983b) The existence of moments for stationary Markov chains. J. Appl. Prob. 20, 191–196.Google Scholar
Walkup, D. and Wets, R. (1969) Lifting projections of convex polyhedra. Pacific J. Math. 28, 465–475.CrossRefGoogle Scholar
Wecker, W. E. (1981) Asymmetric time series. J. Amer. Statist. Assoc. 76, 16–21.Google Scholar