Optimal control of problems governed by abstract elliptic variational inequalities with state constraints. (English) Zbl 0919.49002

Bergounioux, Maïtine

SIAM J. Control Optimization 36, No. 1, 273-289 (1998).

The author investigates optimal control problems governed by elliptic variational inequalities with additional state constraints. The author presents a relaxed formulation for the problem. With penalization methods and approximation techniques he gives qualification conditions to get first-order optimality conditions.

Reviewer: P.Neittaanmäki (Jyväskylä)

MSC:

49J20	Existence theories for optimal control problems involving partial differential equations
49M29	Numerical methods involving duality
35J85	Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49J40	Variational inequalities

Keywords:

state and control constrained optimal control problems; variational inequalities; optimality conditions