Abstract
Nonlinear Variational Inequalities (NVI) have emerged as a powerful mathematical framework for addressing complex optimization problems constrained by Partial Differential Equations (PDEs). This article explores the integration of NVI into PDE-constrained optimization, providing insights into the mathematical foundations, numerical techniques, and practical applications of this synergy. By understanding the role of NVI in PDE-constrained optimization, researchers and practitioners can tackle challenging optimization problems arising in fields such as engineering, physics, and computational science.
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