Naive Question: How to convert max{t,0} to min{.. , ..}

optimization

1,074

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.

1,074

Mohsin

Updated on March 02, 2020

Comments

Mohsin over 3 years

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

$\max\{A,B\}$

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

Thanks.
- jdods over 8 years
  
  $\min\{A,B\}$? I think we need more details about your problem.
- Cameron Williams over 8 years
  
  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.
- Mohsin over 8 years
  
  So it should be $-min\{-t,0\}$? Thanks.
- Mohsin over 8 years
  
  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): $\sigma_{-}(X)^2 = E[-\min\{-(EX - X),0\}^2]$
- jdods over 8 years
  
  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.
- Mohsin over 8 years
  
  Thanks. I will take care of that. Thanks agian.