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

Globally strongly convex cost functional for a coefficient inverse problem