# How to solve this problem with cvx

My convex optimisation problem is of the form minimize z in min \,tr\left\lbrace (H_{M}^{\dagger}H_{M})^{-1}Z\right\rbrace
subject to the constraints:
tr\left\lbrace (H_{E}^{\dagger}H_{E})^{-1}Z\right\rbrace >=\gamma and
tr\left\lbrace Z^{-1}\right\rbrace <= P_{avg}
Here H_{M},H_{E},z are 2x2 matrices. \gamma and P_{avg} are scalars and are known… values of H_{M},H_{E} are also known…
It is also given z is positive definite…
Can someone suggest me how to solve this problem in cvx? Is it possible to solve this problem by using optimisation toolbox in matlab?
What have you tried so far? This forum is not a substitute for reading the manual and trying out the software. The trace and trace_inv commands are both relevant here, as is SDP mode. And it’s a support forum for CVX and TFOCS, not the optimization toolbox.