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As a side benefit, improving the convergence speed also results in savings in energy consumption with respect to the maximally connected setting.
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Clearly, Vε-W A, F) is a nonempty path connected set.
Clearly, V ε (A, F) is a nonempty connected set.
Then, Vε-W A, F) is a path connected set.
On the other hand, obviously, if a set is convex, then it is arcwise connected set.
Since C' is a convex set, so it is a path connected set.
In this paper, the empty set ∅ is assumed to be an arcwise connected set.
Let φ be a real-valued function defined on an arcwise connected set X ⊂ R n.
By Lemma 5.3 and Theorem 5.2, is a nonempty connected set.
It is easy to see that V ε - W ( A, F ) = 0, 2. Clearly, Vε-W A, F) is a nonempty connected set.
If there exists a nonempty compact convex subset of, and, such that, for all, then is a nonempty connected set.
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