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?
Thanks in advance

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.

Sorry for my mistake. I am new to this field. Is it possible to solve this problem in cvx? I am confused because here my optimisation variable z is a 2x2 matrix. z is positive definite also.

Leaving aside other details of the problem, optimization variables which are matrices constrained to be positive definite are right up CVX’s alley.

Right. I suggest that you read the user guide, particularly the function reference, and look at some examples. I am sure you will find that CVX is a good tool for this task. But we’re not a model building service here; we expect you to do the work!