A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems
2020 ◽
Vol 77
(3)
◽
pp. 831-869
Keyword(s):
Abstract In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.
1998 ◽
Vol 38
(3)
◽
pp. 303-325
◽
2017 ◽
Vol 69
(3)
◽
pp. 857-880
◽
2003 ◽
Vol 48
(3-4)
◽
pp. 169-176
◽
2008 ◽
Vol 15
(2)
◽
pp. 471-498
◽
1992 ◽
Vol 33
(4)
◽
pp. 517-530
◽
1990 ◽
pp. 218-234
◽