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In the modern digital economy, optimal decision support systems, as well as machine learning systems, are becoming an integral part of production processes. Artificial neural network training as well as other engineering problems generate such problems of high dimension that are difficult to solve with traditional gradient or conjugate gradient methods. Relaxation subgradient minimization methods (RSMMs) construct a descent direction that forms an obtuse angle with all subgradients of the current minimum neighborhood, which reduces to the problem of solving systems of inequalities. Having formalized the model and taking into account the specific features of subgradient sets, we reduced the problem of solving a system of inequalities to an approximation problem and obtained an efficient rapidly converging iterative learning algorithm for finding the direction of descent, conceptually similar to the iterative least squares method. The new algorithm is theoretically substantiated, and an estimate of its convergence rate is obtained depending on the parameters of the subgradient set. On this basis, we have developed and substantiated a new RSMM, which has the properties of the conjugate gradient method on quadratic functions. We have developed a practically realizable version of the minimization algorithm that uses a rough one-dimensional search. A computational experiment on complex functions in a space of high dimension confirms the effectiveness of the proposed algorithm. In the problems of training neural network models, where it is required to remove insignificant variables or neurons using methods such as the Tibshirani LASSO, our new algorithm outperforms known methods.

The international Global Earth Observation System of Systems is at its initial stage. We present some general information about the program and formulate the task of ensuring the uniformity of radiometric measurements to be conducted by all the participating national systems. Methods of solving the task are suggested on the basis of the wide application of standard sources that use phase transition of eutectic alloys and pure metals as well as with the help of improved ground calibration facilities.

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A necessary condition for accumulating fundamental climate data records is the use of observation instruments whose stability and accuracy are sufficiently high for climate monitoring purposes; the number of instruments and their distribution in space should be sufficient for measurements with no spatial or temporal gaps. The continuous acquirement of data over time intervals of several decades can only be possible under the condition of simultaneous application of instruments produced by different manufacturers and installed on different platforms belonging to one or several countries.The design of standard sources for pre-flight calibrations and in-flight monitoring of instruments has to meet the most stringent requirements for the accuracy of absolute radiometric measurements and stability of all instruments. This means that the radiometric scales should be stable, accurate, and uniform.Current technologies cannot ensure the high requirements for stability and compatibility of radiometric scales: 0.1% per decade within the 0.3 -3 µm band and 0.01 K per decade within the 3 -25 µm band.It is suggested that this task can be aided through the use of the pure metals or eutectic alloy phase transition phenomenon that always occur at the same temperature. Such devices can be used for pre-flight calibrations and for on-board monitoring of the stability of radiometric instruments. Results of previous studies of blackbody models that incorporate phase transition phenomenon are quite promising. A study of the phase transition of some materials in small cells was conducted for future application in onboard monitoring devices and its results are positive and allow us to begin preparations for similar experiments in space.

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