min 1/t
just prints out a meaningless number, and is not contributing to the specification of your optimization problem - i.e., it is essentially ignored by CVX. So you have just been solving a feasibility problem, even though that is not your intention.
You want
minimize(1/t)
But you might as well use
maximize(t)
instead.
I haven’t checked the rest of what you did, so this may not be the only error in your code.
Given you use of gp mode, I recommend you follow the advice at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .