Optimization of Computer Networks by Pavón Mariño Pablo;

Author:Pavón Mariño, Pablo;
Language: eng
Format: epub
Publisher: Wiley
Published: 2016-04-06T00:00:00+00:00

Next proposition states that for the smooth stochastic constant step gradient case, convergence (in expectation) can only be guaranteed to the proximity of the optimum. This is a difference with the deterministic iteration, which could in the smooth case converge to the optimum for a constant, but sufficiently small .

Proposition 8.8

([9], Prop. 5) In problem (8.1), we assume that is a non-empty, closed convex set, is convex and differentiable with Lipschitz gradient with constant , strongly convex with constant 4. Let , in the iteration (8.16). Then, we have

8.19

where is an upper bound to the initial distance to the optimum (), and

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