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Thus the problem we would like to solve is:  \begin{equation*}  \begin{aligned}  & \underset{X}{\text{minimize}} \underset{x}{\text{minimize}}  & & \mathrm{trace}(X) f(x) =  \\ & \text{subject to}  & & X_{ij} = M_{ij}, \; (i,j) \in \Omega, \\  &&& X \succeq 0. 
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