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We consider minimization problems with the well-known Polya-Lojasievichcondition and Lipshitz-continuous gradient. Such problem occurs in differentplaces in machine learning and related fields. Furthermore, we assume that agradient is available with some relative inexactness. We propose some adaptivegradient-type algorithm, where the adaptivity took place with respect to thesmoothness parameter and the level of the gradient inexactness. The theoreticalestimate of the the quality of the output point is obtained and backed up byexperimental results.

Gradient-Type Method for Optimization Problems with Polyak-Lojasiewicz Condition: Relative Inexactness in Gradient and Adaptive Parameters Setting