Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with mixed pointwise constraints
B. T. Kien, Vu Huu Nhu, Arnd Rösch · Optimization · 2014
This paper studies the solution stability of a parametric optimal control problem governed by single linear elliptic equations with mixed control-state constraints and convex cost functions. By reducing the problem to a parametric programming problem and a parametric variational inequality, we obtain sufficient conditions under which the solution map to an elliptic optimal control problem is lower semicontinuous.