Hilbert-Valued Perturbed Subgradient Algorithms

Published Online:https://doi.org/10.1287/moor.1070.0253

References

  • Alber Y., Iusem A., Solodov M. On the projected subgradient method for nonsmooth convex optimization in a Hilbert space. Math. Programming (1998) 81:23–35CrossrefGoogle Scholar
  • Barty K., Roy J.-S., Strugarek C. A stochastic gradient type algorithm for closed loop problems. (2005) Stochastic Programming E-print Series, No. 16. http://www.speps.orgGoogle Scholar
  • Benvéniste A., Métivier M., Priouret P.Adaptive Algorithms and Stochastic Approximation (1990) (Springer Verlag, New York) CrossrefGoogle Scholar
  • Berliocchi H., Lasry J.-M. Nouvelles applications des mesures paramétrées. C. R. Acad. Sci. Paris (1972) 274:1623–1626Google Scholar
  • Bertsekas D. P., Tsitsiklis J. N. Gradient convergence in gradient methods. SIAM J. Optim. (2000) 10(3):627–642CrossrefGoogle Scholar
  • Chen X., White H. Laws of large numbers for Hilbert space-valued mixingales with applications. Econometric Theory (1998) 12:284–304CrossrefGoogle Scholar
  • Chen X., White H. Asymptotic properties of some projection-based Robbins-Monro procedures in a Hilbert space. Stud. Nonlinear Dynam. Econom. (2002) 6:1–53Google Scholar
  • Clark D. S., Kushner H. J.Stochastic Approximation for Constrained and Unconstrained Systems (1978) (Springer Verlag, New York) Google Scholar
  • Cohen G. Décomposition et coordination en optimisation déterministe différentiable et non-différentiable. (1984) . Thèse de doctorat d’État, Université de Paris IX Dauphine, Paris, FranceGoogle Scholar
  • Cohen G., Culioli J.-C. Decomposition coordination algorithms for stochastic optimization. SIAM J. Control Optim. (1990) 28(6):1372–1403CrossrefGoogle Scholar
  • Delyon B. General results on the convergence of stochastic algorithms. IEEE Trans. Autom. Control (1996) 41(9):1245–1255CrossrefGoogle Scholar
  • Derevitskii D., Fradkov A. Two models for analyzing the dynamics of adaptation algorithms. Autom. Remote Control (1974) 35:59–67Google Scholar
  • Duflo M.Random Iterative Models (1997) (Springer Verlag, Berlin, Germany) CrossrefGoogle Scholar
  • Ermoliev Y. Methods of solution of nonlinear extremal problems. Cybernetics (1966) 2(4):1–17CrossrefGoogle Scholar
  • Ermoliev Y. On the method of generalized stochastic gradients and quasi-Féjer sequences. Cybernetics (1969) 5(2):73–84Google Scholar
  • Ermoliev Y.Methods of Stochastic Programming (1976) (Nauka, Moscow, Russia [in Russian]) Google Scholar
  • Goldstein L. Minimizing noisy functionals in Hilbert spaces: An extension of the Kiefer-Wolfowitz procedure. J. Theoret. Probab. (1988) 1:189–204CrossrefGoogle Scholar
  • Hiriart-Urruty J.-B. Algorithmes de résolution d’équations et d’inéquations variationnelles. Z. Wahrscheinlichkeitstheorie verwandte Gebiete (1975) 33:167–186[in French]CrossrefGoogle Scholar
  • Horn C., Kulkarni S. R. An alternative proof for convergence of stochastic approximation algorithms. IEEE Trans. Autom. Control (1996) 41(3):419–424CrossrefGoogle Scholar
  • Kiefer J., Wolfowitz J. Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. (1952) 23:462–466CrossrefGoogle Scholar
  • Lai T. L. Stochastic approximation. Ann. Statist. (2003) 31(2):391–406CrossrefGoogle Scholar
  • Métivier M.Semimartingales (1982) (De Gruyter, Berlin, Germany) CrossrefGoogle Scholar
  • Nevel’son M. B., Has’minskii R. Z.Stochastic Approximation and Recursive Estimation (1973) (American Mathematical Society, Providence, RI) Google Scholar
  • Polyak B. T., Tsypkin Y. Z. Pseudogradient adaptation and training algorithms. Automation Remote Control (1973) 12:83–94Google Scholar
  • Révész P. Robbins-Monro procedure in a Hilbert space and its application in the theory of learning processes. I.. Studia Scientiarum Mathematicarum Hungarica (1973) 8:391–398Google Scholar
  • Révész P. Robbins-Monro procedure in a Hilbert space. II.. Studia Scientiarum Mathematicarum Hungarica (1973) 8:469–472Google Scholar
  • Robbins H., Monro S. A stochastic approximation method. Ann. Math. Statist. (1951) 22:400–407CrossrefGoogle Scholar
  • Robbins H., Siegmund D., Rustagi J. S. A convergence theorem for nonnegative almost supermartingales and some applications. Optimizing Methods in Statistics (1971) (Academic Press, New York) 233–257Google Scholar
  • Salov G. On a stochastic approximation theorem in a Hilbert space and its applications. Theory Probab. Appl. (1980) 24:413–419CrossrefGoogle Scholar
  • Yin G., Zhu Y. M. On H-valued Robbins-Monro processes. J. Multivariate Anal. (1990) 34:116–140CrossrefGoogle Scholar
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