[Csdp] hinge loss with slack variables

[Nicolas Bock]

I am sorry, I oversimplified the problem. Suppose the cost function is more
complicated, and looks something like this:

max_{X} Tr( C_{1} X + [ C_{2} X ]_{+} )

Thanks,

nick



On Thu, Aug 8, 2013 at 5:41 PM, Brian Borchers <borchers at nmt.edu> wrote:

>
>
>
> 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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