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I am reading a paper where the authors made the following statement on page 16: enter image description here

I wonder why dropping the 'min' operator inside a 'max' objective function is a valid operation here. Any explanation with simple example will be highly appreciated.

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  • $\begingroup$ Hi @Apurba Saha and welcome to or.stackexchange. I think you would get better responses if you link to the paper your are reading. From the context in your question it will be difficult to answer. $\endgroup$
    – Sune
    Commented Jan 9 at 9:46
  • $\begingroup$ It does not answer your question, but seems the "min" operator is outside the "max" objective. $\endgroup$
    – Mostafa
    Commented Jan 12 at 9:19

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A simple intuition would be that the second inequality is stronger ($\geq$) than the first one. Therefore, dropping the minimum would allow more flexibility, but I do not think they are equivalent.

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