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The 2D localization inverse problem of mathematical geophysics is considered. It is of kind of so-called gravimetric problems, due to the underlying process of primary data gathering, the gravimetry. The latter is systematically fulfilled measuring of the gravitational field on the Earth's surface with special high-precision digital appliances, gravimeters. By virtue of the known Poisson equation, which ties together the gravitational potential and material density, the measured fluctuations of potential gravitational field might point on the increase or decrease of material density under Earth's surface, therefore, indicating, for example, desired mineral fields, or underground voids, filled with liquid or gas (which is not always desired, and even can be dangerous). Here we have to accomplish a coordinate recovery for homogeneous gravitational anomaly by the results of gravimetry. In this work we show that minimization process here isn't trivial: the functional has a derivative in any direction, but its classic gradient does not exist. So, then we should switch on non-gradient methods instead. For the numerical solution of the problem, we applied subsequently the subgradient, Nelder-Mead, and the genetic algorithms. Based on results of these computations, a comparative analysis of the applied algorithms is conducted. Also, here we propose corresponding subgradient esteems and the ready-to-use subgradient formulae for numerical solving of this problem. [ABSTRACT FROM AUTHOR]