How can I write the following term t in cvxquad?

I want to ask you if it is possible please guide me.

I want to write t=((abs(a))^p+small constant)/(small constant +a^2) in cvxquad, where p is cvx variable 1=< p<2 and a is constant but its value changes in each iteration . but I cannot keep its boundedness feature when a=0 in my formulation in cvxquad.
This term should be used in
min trace_inv(A’*diag(t)*A) where , A is known semidefinit matrix.
as we see if the boundedness of t does not keep, the optimal value of optimization get inf.
how can I formulate t in cvxquad?

This doesn’t appear to have anything to with CVQUAD, which is an add-on collection of functions for use in CVX.

And it doesn’t appear to really be a CVX matter, even if you are using CVX. It sounds like you are using Successive Convex Approximation (SCA), and SCA is not performing as you wish. It is not generating a successful series of problems for CVX to solve. Unsafeguarded SCA can be unstable and unreliable - you can search on this forum for posts where I discuss that at greater length. You might be better off using a high quality off-the-shelf non-convex optimizer.