Kulkarni, Ankur A. ; Borkar, Vivek S.
(2009)
*Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space*
Automatica, 45
(12).
pp. 2815-2822.
ISSN 0005-1098

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.automatica.2009.09.031

## Abstract

This paper presents a finite dimensional approach to stochastic approximation in infinite dimensional Hilbert space. The problem was motivated by applications in the field of stochastic programming wherein we minimize a convex function defined on a Hilbert space. We define a finite dimensional approximation to the Hilbert space minimizer. A justification is provided for this finite dimensional approximation. Estimates of the dimensionality needed are also provided. The algorithm presented is a two time-scale Newton-based stochastic approximation scheme that lives in this finite dimensional space. Since the finite dimensional problem can be prohibitively large dimensional, we operate our Newton scheme in a projected, randomly chosen smaller dimensional subspace.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Stochastic Approximation; Hilbert Spaces; Stochastic Programming; Convex Optimization; Random Projection |

ID Code: | 81473 |

Deposited On: | 07 Feb 2012 05:01 |

Last Modified: | 07 Feb 2012 05:01 |

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