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Rates of Ideal Convergence for Approximation Operators
Mediterranean Journal of Mathematics, 2010This paper presents some convergence results on the Korovkin-type approximation theory when the notion of \({\mathcal I}\)-convergence is used, where \({\mathcal I}\) is an ideal in \(\mathbb N\) such that \(\{n\}\in{\mathcal I}\), \(n\in\mathbb N\). This new type of convergence was introduced by \textit{P. Kostyrko, T. Šalát} and \textit{W. Wilczynski}
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Budget-Dependent Convergence Rate of Stochastic Approximation
SIAM Journal on Optimization, 1998Summary: Convergence rate results are derived for a stochastic optimization problem where a performance measure is minimized with respect to a vector parameter \(t\). Assuming that a gradient estimator is available and that both the bias and the variance of the estimator are (known) functions of the budget devoted to its computation, the gradient ...
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