No abstract

No abstract

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with a built-in algorithm for finding the descent direction that forms an acute angle with all subgradients in the neighborhood of the current minimum. Minimizing the function along the opposite direction (with a minus sign) enables the algorithm to go beyond the neighborhood of the current minimum. The family of algorithms for finding the descent direction is based on solving systems of inequalities. The finite convergence of the algorithms on separable bounded sets is proved. Algorithms for solving systems of inequalities are used to organize the RSM family. On quadratic functions, the methods of the RSM family are equivalent to the conjugate gradient method (CGM). The methods are intended for solving high-dimensional problems and are studied theoretically and numerically. Examples of solving convex and non-convex smooth and non-smooth problems of large dimensions are given.

This article provides a comparison of biogas plants for waste processing of various modifications, advantages and disadvantages, as well as a description of a biogas plant of its own development of a horizontal type, taking into account local climatic and economic conditions of farm development, in the context of a pandemic. The article discusses of using of our patented pneumatic motor for mixing biowaste, the bioreactor of own production and comparing the development of biogas station in different countries.

No abstract