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If we have a constraint optimization problem in which one of our constraint is $\prod\limits_{k = 1}^N {\left( {x - {a_k}} \right) = 0} $ . How could this nonlinear equality condition be changed into a combination of some conic inequality constraint and rank constraint??

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  • $\begingroup$ Let $A = diag(a_1, ..., a_N)$ and $I$ be the identity. Then, your constraint becomes $rank(xI - A) = 0$. No need for conic inequality constraints. $\endgroup$
    – rodms
    Commented Aug 11, 2014 at 1:43

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