[Csdp] hinge loss with slack variables

[Nicolas Bock]

Hi,

Suppose I would like to maximize

max_{X} [ Tr(C X) ]_{+}

where [z]_{+} = max(z, 0), the hinge loss function. I can replace the hinge
loss with a slack variable and get

max_{X} \xi
s.t.
\xi >= Tr(C X)

But turning the inequality constraint into an equality constraint would
require another slack variable, i.e.

max_{X} \xi
s.t.
\xi - \eta - Tr(C X) = 0

Is that the right approach? The fact that I now have two slack variables,
and use only one in the cost function strikes me as potentially problematic.

Thanks already,

nick
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