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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Hybrid optimization method for solving Bayesian inverse problems in conditions of complete uncertainty
Creators: name: ÐÐ°Ð¼Ð¸ÑÐ¾Ð²Ð°, Ð¡Ð°Ð±Ð¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
Ð±Ð°Ð¹ÐµÑÐ¾Ð²ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð´Ñ Ð¾Ð´
Ð¾Ð±ÑÐ°ÑÐ½ÑÐµ Ð±Ð°Ð¹ÐµÑÐ¾Ð²ÑÐºÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸
Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ
ÑÑÐ¾Ñ Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð³ÑÐ°Ð´Ð¸ÐµÐ½Ñ
ÐºÐ¾Ð½ÐµÑÐ½Ð°Ñ ÑÐ°Ð·Ð½Ð¾ÑÑÑ
Ð³Ð¸Ð±ÑÐ¸Ð´Ð½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
optimization algorithms
bayesian approach
inverse bayesian problems
linear optimization
stochastic gradient
finite difference
hybrid optimization algorithm

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description: Theme of the final qualification work: Â«A hybrid optimization method for solving Bayesian problems in conditions of complete uncertaintyÂ».
In this paper, we consider existing optimization algorithms such as the finite-difference method and the stochastic optimization algorithm based on the directional derivative. Based on these algorithms, a new hybrid algorithm is created.
The main idea of the hybrid algorithm is to first calculate the stochastic gradient of the objective function using the stochastic optimization algorithm based on the directional derivative, and then replace the components with the largest stochastic gradient with approximate gradient values from the finite difference into the correct sequence until the direction of the changed gradient is almost the same as the unknown direction of the real gradient.
Chapter 1 explains the idea of the Bayesian approach and Bayesian inverse problems in the face of uncertainty. Chapter 2 discusses the linear optimization method and the stochastic optimization algorithm based on the directional derivative. Chapter 3 provides a hybrid algorithm based on the algorithms mentioned above. Chapter 4 demonstrates how the algorithm works and identifies improvements for the hybrid method.
As a result of the work, a hybrid optimization method was developed that allows optimizing the solution of Bayesian inverse problems under conditions of complete uncertainty.