Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. (English) Zbl 1037.49024

Casas, Eduardo; Mateos, Mariano

SIAM J. Control Optimization 40, No. 5, 1431-1454 (2002).

The authors present first and second order optimality conditions for optimal control problems of a semilinear equation of elliptic type, with Neumann boundary conditions and a distributed control. There are also bound control constraints as well as a finite number of abstract constraints on the state. They prove the equivalence of Lagrangian and Hamiltonian formulations.

Reviewer: Joseph Frédéric Bonnans (Le Chesnay)

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J60	Nonlinear elliptic equations

Keywords:

optimal control; semilinear elliptic equations; optimality conditions; state constraints