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Perhaps it is a very basic question, I want the following in $min$ form:

$\max\{A,B\}$

What is the equivalent $\min\{.,.\}$ formulation?

Thanks.

Mohsin
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    $\min{A,B}$? I think we need more details about your problem. – jdods Mar 10 '15 at 14:17
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    Here's a way to do it for the example in the title. I'll leave you to figure out how to do it in general. $-min{-t, 0}$ is the answer you're looking for. – Cameron Williams Mar 10 '15 at 14:17
  • So it should be $-min{-t,0}$? Thanks. – Mohsin Mar 10 '15 at 14:18
  • I want the formulation of Semi-variance in min form. It is given as:

    $\sigma_{-}(X)^2 = E[\max{EX - X,0}^2]$

    I am looking for the above definition in $min$ form so something like (according to the above suggestion):

    $\sigma_{-}(X)^2 = E[-\min{-(EX - X),0}^2]$

     – Mohsin Mar 10 '15 at 14:19
  • Next time, you might consider adding these highly relevant details to your original question! Asking the question in the body and not just in the title would be helpful to potential answerers as well. – jdods Mar 10 '15 at 14:25
  • Thanks. I will take care of that. Thanks agian. – Mohsin Mar 10 '15 at 14:28

2 Answers2

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You may use the following relationship $$ \inf_{x\in\mathcal{X}}\{x\} = -\sup_{x\in\mathcal{X}}\{-x\} $$ where $\mathcal{X} = \{A,B\}$. See here for details.

jjjjjj
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max{A,B} = 1 - min{1 - A, 1- B}, I think

Keren
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