The first constraint would be an Second Order Cone constraint if t were input data. It is a non-convex constraint when t is an optimization (decision) variable. In the image,t should be listed as an optimization variable, because otherwise, maximizing it would not make sense (or it would just be a feasibility problem).
The problem is non-convex as written. So it either needs to be solved as a non-convex problem (you can try using YALMIP), or perhaps it is meant as part of an iterative scheme by which t is iterated or gridded, in which case maybe it is intended only as a feasibility problem, in which case including an objective of max t contributes to confusion.
Perhaps you need to study the paper or book you found this in more carefully.