  A Carleman Weight Function (CWF) is used to construct a new cost functional
for a Coefficient Inverse Problems for a hyperbolic PDE. Given a bounded set of
an arbitrary size in a certain Sobolev space, one can choose the parameter of
the CWF in such a way that the constructed cost functional will be strongly
convex on that set. Next, convergence of the gradient method, which starts from
an arbitrary point of that set, is established. Since restrictions on the size
of that set are not imposed, then this is the global convergence.
