Is there ether on it ?

https://fezzamania.wordpress.com/2018/06/07/skilas-buku-pentagon-aliens-1/

.

By perturbations of problem A by means problem B

,

where is a non-decreasing -order-convex function on a partially set and .

Let be a guaranteed error estimate for the gradient algorithm in some unperturbed (perturbed) discrete optimization problem. As usual (see. [3]), we say that the gradient algorithm is stable if , where as .

Theorem. Let and be guaranteed error estimates for the gradient algorithm in Problems A and B, respectively. Then .

To prove Theorem, we need the following lemma.

Lemma. The gradient maximum and the global maximum of any -ordered-convex non-decreasing function on are connected by the following relations:

, (1)

where

– is the set of all maximal elements of the partially ordered set .

Proof of Lemma. By virtue of item of Theorem 4 [4], we have for

Together with the fact that

the last inequality yields

.

Therefore

,

Where

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My last LHC status update | The Everything Seminar

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