(non)linear programming with optional constraints

1. Jan 6, 2010

coolnessitself

I'm not sure if this is the best forum for this post, but no single forum seems to be a better fit, and I bet the members here are familiar with the topic.

I have a problem of the form
\begin{flalign*} \min &\qquad& c^Tx \\ \mbox{subject to} &\qquad&Ax\ge b \\ &&Cx = d \\ &&Ex = f \end{flalign*}
and I'm looking for a way to require that $$Ax\ge b$$ is held, $$Ex=f$$ is held, and from $$Cx=d$$, one constraint is chosen as part of a solution vector, and the others are ignored. Whether or not a specific row of $$Cx=d$$ is chosen is up to the objective function.
I might think that an MLCP would allow this formulation, but does anyone have further suggestions?

Last edited: Jan 6, 2010