SIAM Journal on Control and Optimization, Vol.45, No.2, 548-564, 2006
Existence of regular Lagrange multipliers for a nonlinear elliptic optimal control problem with pointwise control-state constraints
A class of optimal control problems for semilinear elliptic equations with mixed control-state constraints is considered. The existence of bounded and measurable Lagrange multipliers is proven. As a particular application, the Lavrentiev-type regularization of pointwise state constraints is discussed. Here, the existence of associated regular multipliers is shown, too.
Keywords:nonlinear programming;function space;optimal control;Lagrange multiplier;semilinear elliptic equation;mixed control-state constraint;pointwise state constraint;Lavrentiev-type regularization