Suggestion on how to implement this problem

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Dec 14, 2018, 5:45:46 AM12/14/18

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I have this problem solve:

$min_{x\in S} \left|\left|\left(\begin{bmatrix} I_n\\ (A(x)+B(x))^{-1}(C(x)+D(x))\\ \end{bmatrix}\right)^+ a -b\right|\right|^{2}$

if x are sdpvars, how to handle the inversion of A(x), B(x) and the pseudo inverse in Yalmip optimization?

a and b are constant vectors while E is a constant matrix.

x are bounded from simple linear inequalities.

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Dec 14, 2018, 5:48:59 AM12/14/18

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$min_{x\in S} \left|\left|\left(E\begin{bmatrix} I_n\\ (A(x)+B(x))^{-1}(C(x)+D(x))\\ \end{bmatrix}\right)^+ a -b\right|\right|^{2}$

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Dec 14, 2018, 7:07:02 AM12/14/18

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I don't see any nice way to represent that, due to inverse and the max(0,z) operator

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