Inverse Problems with Nonlinear Variational Inequalities

Abstract

Inverse problems are a class of challenging mathematical problems that involve estimating the properties or parameters of a system from observed data. In recent years, Nonlinear Variational Inequalities (NVI) have emerged as a powerful framework for solving inverse problems with complex constraints. This article explores the application of NVI to inverse problems, discussing their mathematical foundations, computational techniques, and real-world applications. By understanding the role of NVI in inverse problems, researchers and practitioners can tackle a wide range of problems in fields such as imaging, geophysics, and medical diagnostics.