Accumulation point

Sequences and Their Limits

Published in John Srdjan Petrovic, Advanced Calculus, 2020

We see that, when the sequence is convergent, it has only one accumulation point (its limit). Can there be a sequence without any accumulation points? Recall that, by the Bolzano—Weierstrass Theorem, if a sequence is bounded, it must have an accumulation point. So, we had better look at an unbounded sequence.

Improved convergence analysis of a smoothing Newton method for the circular cone programming

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Journal Information

Published in Optimization, 2022

Jingyong Tang, Jinchuan Zhou

Let . Then the following results hold. For any , we have .For any , if and only if v = 0.For any sequence , let be an accumulation point of the sequence , then . Furthermore, if is bounded below and as , then .

Accumulation point

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Sequences and Their Limits

Improved convergence analysis of a smoothing Newton method for the circular cone programming