ABSTRACT
This work is an overview of some of the recent developments in regularization methods for optimal control problems for partial differential equations with pointwise state constraints. One of the central issues in such control problems is that the low regularity of the associated Lagrange multipliers has a negative impact on their adequate treatment and regularization methods are helpful. Although we will discuss several regularization methods, the main focus will be on the conical regularization and its analogs. We will also consider an extension of the conical regularization to variational inequality constrained optimization, Nash equilibrium problems, and supply chains on networks. This work highlights a cross-fertilization of the ideas between optimal control and variational analysis.
