Название: Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications
Автор: Joachim Gwinner, Baasansuren Jadamba
Издательство: CRC Press
Год: 2022
Страниц: 405
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to Machine Learning (ML), neural networks, and related fields.

In the last several decades, the theory of variational inequalities emerged as one of the most promising branches of pure, applied, and industrial mathematics. This theory provides us with an efficient mathematical apparatus for studying a wide range of problems arising in diverse fields such as mechanics, elasticity, economics, optimization, finance, and others. However, the vast majority of studies on variational inequalities have focused on deterministic models. Since in real-world applications, the data are often impacted by uncertainty, their variational inequality formulations must consider this stochasticity. Consequently, it is now a well-accepted fact that the role of uncertainty cannot be overlooked in models that rely on data.

This book, which is the first systematic and comprehensive treatment of variational inequalities with random data, presents some of the commonly used techniques for uncertainty quantification and applications to applied models. Aiming for a diverse audience, including applied mathematicians, engineers, economists, and professionals from academia, we present the material in a self-contained and lucid style. The given results include the most recent developments on the subject, most of which so far have only been available in the research literature.