In the proposed paper one of the approaches to automation of the gradient descent method based on the pre-calculated local geometrical characteristics of space of a function is considered. We represent the local geometrical characteristics by a set of voxel images co-dimensional to this space. Computer geometrical models obtained by means of the Functional Voxel method form the informational basis for the algorithm. The main principles of the gradient motion control along with the peculiarities of the conversion to increase the problem dimensionality are demonstrated. The detected advantages of the algorithm allow to extend the usage of such approach from the mathematical programming problems towards the local optimization on the example of laying the route for the steepest descent.