On Convergence of Iterated Random Maps
| Autor: | John R. Liukkonen, Arnold Levine |
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| Rok vydání: | 1994 |
| Předmět: | |
| Zdroj: | SIAM Journal on Control and Optimization. 32:1752-1762 |
| ISSN: | 1095-7138 0363-0129 |
| DOI: | 10.1137/s0363012992238977 |
| Popis: | Let $K$ be a compact subset of ${bf R}^N$ consisting of an open subset of ${\bf R}^N$ and smooth boundary. Many stochastic optimization algorithms can be viewed as iterations of independent and identically distributed random elements of the continuous self-maps of such a $K$. In case the target of the algorithm is a single point $\bf p$, a near dichotomy for the convergence to $\bf p$ is given; roughly, if ${\bf M}_1$ is one of the random elements, then there will be no convergence in probability if $E(\log \|\hbox{\bf M}_{1}^{\prime}(\hbox{\bf p})\|)>0,$ but there will be almost sure convergence if $E(\log \|{\bf M}_{1}^{\prime}(\hbox{\bf p})\|) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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