  A version of the so-called "convexification" numerical method for a
coefficient inverse scattering problem for the 3D Hemholtz equation is
developed analytically and tested numerically. Backscattering data are used,
which result from a single direction of the propagation of the incident plane
wave on an interval of frequencies. The method converges globally. The idea is
to construct a weighted Tikhonov-like functional. The key element of this
functional is the presence of the so-called Carleman Weight Function (CWF).
This is the function which is involved in the Carleman estimate for the Laplace
operator. This functional is strictly convex on any appropriate ball in a
Hilbert space for an appropriate choice of the parameters of the CWF. Thus,
both the absence of local minima and convergence of minimizers to the exact
solution are guaranteed. Numerical tests demonstrate a good performance of the
resulting algorithm. Unlikeprevious the so-called tail functions globally
convergent method, we neither do not impose the smallness assumption of the
interval of wavenumbers, nor we do not iterate with respect to the so-called
tail functions.
