What does a function inside brackets and a minus sign mean?

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I am working in constraint optimization. And I've just come across this notation.

I'm not sure what this means.

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The set I is the set of inequality constraints. I'm not sure what the function in brackets means

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I guess that $[y]^- = \min(y,0)$.

This notation is mentioned in Wikipedia, but with a slight difference: $[y]^- = -\min(y,0)$.

The important point is the minus sign as a superscript. The brackets are just like parentheses.