Analysis and approximation of optimal control problems with nonlinear constraints

A general framework for treating nonlinearly constrained optimal control and optimization problems is given. Based on a set of hypotheses, optimal solutions are shown to exist and the use of language multipliers to enforce the constraints is justified. An optimality system is derived whose solutions provide the optimal states and controls. Finite dimensional approximations are then considered: an approximate problem is defined, and optimal error estimates are derived. The general framework has been applied to numerous concrete settings. We illustrate its use in the context of a magnetohydrodynamics control problem