[Csdp] hinge loss with slack variables

[Brian Borchers]

On Thu, Aug 8, 2013 at 3:38 PM, Nicolas Bock <nicolasbock at gmail.com> wrote:

> Hi,
>
> Suppose I would like to maximize
>
> max_{X} [ Tr(C X) ]_{+}
>
> where [z]_{+} = max(z, 0), the hinge loss function.
>


You can simply maximize

  max_{X} Tr(CX)

subject to whatever constraints you have.

if the optimal value is negative, then that optimal solution is still
optimal for your original objective with the optimal value of Tr(CX)_{+}=0.

If the optimal value is nonnegative, then optimal solution to the Tr(CX)
problem is still optimal for the original problem.

There's no need to add a slack variable.


-- 
Brian Borchers                          borchers at nmt.edu
Department of Mathematics      http://www.nmt.edu/~borchers/
New Mexico Tech                       Phone: (575) 322-2592
Socorro, NM 87801                   FAX: (575) 835-5366
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