26
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Optimal quasi-convex combinations for stochastic approximation algorithms with parallel observers

&
Pages 1947-1964 | Received 13 Jan 1988, Published online: 01 Apr 2008

References

  • Chen , H. F. 1985 . Recursive Estimation and Control for Stochastic Systems , New York : Wiley .
  • Chen , H. F. , and Zhu , Y. M. 1986 , Stochastic approximation procedure with randomly varying truncations . Scientia Sinica (series A) , 29 , 914 – 926 ; 1987, Asymptotic properties of a stochastic approximation algorithm with randomly varying truncations. Acta Mathematica Scientia, 7, 431-441 .
  • Chow , Y. S. 1965 . Local convergence of martingales and the law of large numbers . Annals of Mathematical Statistics , 36 : 552 – 558 .
  • Graham , A. 1981 . Kronecker Products and Matrix Calculus with Applications , New York : Horwood .
  • Kiefer , E. and Wolfowitz , J. 1952 . Stochastic estimation of the maximum of a regression function . Annals of Mathematical Statistics , 23 : 462 – 466 .
  • Kushner , H. J. 1984 . Approximation and Weak Convergence Methods for Random Processes with Applications to Stochastic Systems Theory , Cambridge, Mass : MIT Press .
  • Kushner , H. J. and Clark , D. S. 1978 . Stochastic Approximation Methods for Constrained and Unconstrained Systems , Berlin : Springer-Verlag .
  • Kushner , H. J. , and Yin , G. 1987 a , Asymptotic properties of distributed and communicating stochastic approximation algorithms . SIAM Journal on Control and Optimization , 25 , 1266 – 1290 ; 1987b, Stochastic approximation algorithms for parallel and distributed processing. Stochastics, 22, 219-250 .
  • Ljung , L. 1977 . Analysis of recursive stochastic algorithms . I.E.E.E. Transaction on Automatic Control , 22 : 551 – 575 .
  • Nevelson , M. B. and Hasminskii , R. Z. 1976 . Stochastic Approximation and Recursive Estimation, Translation of Math Monographs , Vol. 47 , Providence, RI : American Math. Soc .
  • Robbins , H. and Monro , S. 1951 . A stochastic approximation method . Annals of Mathematical Statistics , 22 : 400 – 407 .
  • Ruppert , D. 1985 . A Newton-Raphson version of the multivariate Robbins-Monro Procedure . Annals of Statist. , 13 : 236 – 245 .
  • Tsitsiklis , J. N. 1984 , Problems in decentralized decision making and computation . Ph.D. thesis, Elect. Engng Dept, M.I.T., Cambridge, MA .
  • Venter , J. H. 1967 . An extension of the Robbins-Monro procedure . Annals of Mathematical Statistics , 38 : 181 – 190 .
  • Yin , G. , and Zhu , Y. M. 1989a , On w.p.1 convergence of a parallel stochastic approximation algorithm . Probability in the Engineering and Informational Sciences , 3 , 55 – 75 ; 1989b, Almost sure convergence of stochastic approximation algorithms with non-additive noise. International Journal of Control, 49, 1361-1376 .
  • Zhu , Y. M. 1985 . Extensions of the relations of series to infinite products and the convergence of a class of recursive algorithms . Mathematica Numerica Sinica , 7 : 369 – 376 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.