Problems of multidimensional multiextremal optimization and numerical methods for their solution are considered. The general assumption is made about the function being optimized: it satisfies the Lipschitz condition with an a priori unknown constant. Many approaches to solving problems of this class are based on reducing the dimension of the problem; i.e. addressing a multidimensional problem by solving a family of problems with lower dimension. In this work, an adaptive dimensionality reduction scheme is investigated, and its implementation using graphic accelerators is proposed. Numerical experiments on several hundred test problems were carried out, and they confirmed acceleration in the developed GPU version of the algorithm.