Uncertainty Quantification in Variational Inequalities
Theory, Numerics, and Applications
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Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively delineate any uncertainty in applied models. The primary objective of this book is to present a comprehensive treatment of uncertainty quantification in variational inequalities (and some of its generalizations such as quasi-variational inequalities) emerging from various network, economic, and engineering models.
Table of Contents
Introduction. Introduction to Variational Inequalities. Numerical Methods for Variational Inequalities. Tools from Probability. Uncertainties in Variational Inequalities. Sample Path Based Approaches. Traffic Equilibrium Problem. Spatial Price Equilibrium Problems. Nash equilibrium problems. Generalized Nash equilibrium problems and Environmental Games. Migration Equilibrium Models. Stochastic Lagrange Multipliers.
B. Jadamba is affiliated with the School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York. Her primary research interest is in uncertainty quantification in network models, variational inequalities, and inverse problems. She has published more than 30 scientific papers.
Akhtar Khan, an Associate Professor at the School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York, focuses on set-valued optimization, variational and quasi-variational inequalities, inverse problems and uncertainty quantification. He is the co-author of the monograph Set-Valued Optimization: Theory, methods and applications, published by Springer in 2014. Khan is the Associate Editor of the prestigious international journals Optimization and Journal of Optimization Theory and Applications. He has published more than 60 scientific papers.
Fabio Raciti is associated with the Department of Mathematics and Computer Science of the University of Catania, Italy, where he also teaches various calculus courses for engineering students. In 2013 he obtained the rank ( Italian habilitation) of associate professor of Operations Research. He is an Associated Editor of the journal Optmization. His research interests are in uncertainty quantification in network models, variational inequalities, duality theory, set convergence, inverse problems, and quantum mechanics. He has published more than 50 research papers