 Lower semicontinuity (source code)

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= Lower semicontinuity

= Lower semicontinuous
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A function is lower semicontinuous when its strict superlevel sets are open, equivalently when its sublevel sets are closed. In Euclidean spaces this is the <sequential lower semicontinuity> condition $f(x)\leq\liminf_k f(x_k)$ whenever $x_k\to x$. This closedness property is essential to existence of proximal minimizers.

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