Dual of a particular semidefinite program

(Will Shaw) #1

I have a semidefinite program of the form
\min_A \text{Tr}(A^TB)
subject to
\lvert{\text{Tr}(C_1A)-c_1\rvert}^2 + \lvert{\text{Tr}(C_2A)-c_2\rvert}^2 + ... + \lvert{\text{Tr}(C_nA)-c_n\rvert} ^2\leq M
A \succeq 0
where A is Hermitian.

CVX handles the model just fine and yields accurate result. It frequently converts to the dual problem. I understand how to get the dual for constraints of the form \lvert{\text{Tr}(C_iA)-c_i\rvert}^2<M with only the one term. My question is this: what is the dual semidefinite program of the problem above? I can’t figure out what sort of slack variables might be introduced.

(Michael C. Grant) #2

This is not the proper forum for this question, as it is not CVX-specific. I suggest asking this question on Math StackExchange.

(Michael C. Grant) #3