An algorithm of approximation of a multidimensional point by point scalar function is considered. The solution is sought as a series in a set of basis functions. The approximation is regular ized by the introduction of a stabilizing function in the Gaussian form; the parameter of regularization is sought by using the Bayesian approach. The proposed algorithm is inexpensive in terms of compu tations. Unlike other Bayesian models of approximation, it has a unique analytical solution for the reg ularization parameters.

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The paper proposes a mathematical model to optimize the operation of the tar hydrocracking unit. The purpose of modeling is to improve the economic effect of product output by selecting optimal parameters, such as hydrogen flow rate and reactor temperature. Hot Filtered Precipitation (HFT) is used as a target. The model involves the search for the minimum value of the functional with restrictions presented in the form of a fine imposed when the parameters go beyond the permissible values, as well as when the target parameter deviates from the specified value. The execution of the algorithm includes two stages. The first stage is the simulation of the HFT value for a given state of the installation at the selected parameters of temperature and hydrogen flow rate using a virtual analyzer, the second stage is to solve the optimization problem by selecting the control parameters of the installation. For the first stage, a model for assessing the HFT indicator by technological indicators was built, including the main factors determining it; machine learning methods were used to find the parameters of the models. The free standard library of optimum search tools scipy.optimize was used to solve the optimization problem. Powell's algorithm was chosen as the optimization method. The paper presents the results of testing the model on real data provided by an oil refinery in the city of Burgas in Bulgaria. The study period includes several operating modes of the installation, in particular, the intensive load mode during 2018-2019 and low load during the 2020 period. The results of testing the model on real data presented in the work have been verified by experts in the field of oil refining for compliance with real conditions.