ИСТИНА

Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly for an arbitrary point in the parameter space. Typically, this problem is solved by pre-computing a grid of models for a predetermined set of positions in the parameter space, which are then interpolated between grid nodes to achieve continuous and differentiable behavior of the evaluated function required by gradient optimization methods. In case of complex models (e.g. spectra of stars or stellar populations) a significantly non-linear rapid change in the shape of a model lead to systematic artifacts hampering the minimization quality, e.g. by trapping a solution to some "magic" values. Here we present a hybrid minimization approach based on the local quadratic approximation of the chi2 profile from a discrete set of models in a multidimensional parameter space. The main idea of our approach is to eliminate the interpolation of models from the process of finding the best-fitting solution. The algorithm includes: (i) constructing a connectivity matrix for a grid of models; (ii) checking connected nodes and choosing a node with a minimum value of chi2 using a downhill/uphill climbing algorithm; (iii) finding an off-node solution from the approximation of chi2 values at connected nodes with a positively definite quadratic form, (iv) determination of weights for the superposition of models at the minimum position. This approach allows us to deal with irregular multidimensional grids of models, provided there is a local basis for the required dimension. In addition to the discrete parameters of the models, one can minimize continuous functional parameters (such as Doppler radial velocities, rotational broadening for stars) at each tested node using standard gradient methods. The result is a simultaneous determination of discrete (for stellar spectra: Teff, log g, [Fe/H]) and continuous (for stellar spectra: v, vsini) parameters of the models. We present several examples of the applications of this minimization technique to the analysis of spectra of stars (VOXAstro stellar libraries) and galaxies (RCSED catalog) and compare them to "standard" approaches, which use interpolation in regularly spaced model grids -- they clearly demonstrate advantages of our method over standard techniques.