Some Optimal Control Problems Governed by Elliptic Variational Inequalities with Control and State Constraint on the Boundary

2000 ◽  
Vol 106 (3) ◽  
pp. 627-655 ◽  
Author(s):  
G. Wang ◽  
Y. Zhao ◽  
W. Li
Keyword(s):  
Optimal Control ◽  
Variational Inequalities ◽  
Optimal Control Problems ◽  
State Constraint ◽  
Control Problems ◽  
Elliptic Variational Inequalities

scholarly journals A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems

2020 ◽  
Vol 77 (3) ◽  
pp. 831-869
Author(s):  
Veronika Karl ◽  
Ira Neitzel ◽  
Daniel Wachsmuth
Keyword(s):  
Optimal Control ◽  
Weak Convergence ◽  
Original Problem ◽  
Optimal Control Problems ◽  
State Constraint ◽  
Stationary Points ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Semilinear Elliptic ◽  
Augmented Lagrange Method

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.

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