Name
Title | ||
|---|---|---|
Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space |
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.automatica.2009.09.031 | Automatica |
Keywords | Field | DocType |
Stochastic approximation,Hilbert spaces,Stochastic programming,Convex optimization,Random projection | Hilbert space,Mathematical optimization,Random field,Subspace topology,Mathematical analysis,Algorithm,Curse of dimensionality,Hilbert manifold,Convex function,Convex optimization,Stochastic approximation,Mathematics | Journal |
Volume | Issue | ISSN |
45 | 12 | Automatica |
Citations | PageRank | References |
1 | 0.36 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ankur A. Kulkarni | 1 | 106 | 20.95 |
| Vivek S. Borkar | 2 | 974 | 142.14 |