I believe that when called with a matrix argument, norms only allows the 2nd argument to be 1, 2, or inf, although that doesn’t seem to be documented. Hence the rather cryptic error message,
However, I believe you can accomplish what you want with this brute force approach.
Obj = 0;
for i = 1:5
Obj = Obj + norm(z(i,:),2.5);
end
minimize(Obj)
Obviously this program as written doesn’t make sense as the final program, because optimal z will always be all zeros. I presume you will want to bring b into the objective. I will let you figure out in what manner and with appropriate dimensions for everything.