  We consider minimization problems with the well-known Polya-Lojasievich
condition and Lipshitz-continuous gradient. Such problem occurs in different
places in machine learning and related fields. Furthermore, we assume that a
gradient is available with some relative inexactness. We propose some adaptive
gradient-type algorithm, where the adaptivity took place with respect to the
smoothness parameter and the level of the gradient inexactness. The theoretical
estimate of the the quality of the output point is obtained and backed up by
experimental results.

Optimization and Control