Optimal control and approximation for elliptic bilateral obstacle problems
This paper studies a nonlinear elliptic bilateral obstacle system with a multivalued term given by Clarke's generalized gradient. The existence and uniqueness of weak solution to this problem is obtained, through its formulation as a variational-hemivariational inequality. In addition, a corresponding nonlinear optimal control problem governed by the elliptic system is considered, in which the control variable is the bilateral obstacle, and the existence of an optimal solution is obtained. Then, employing the regularization technique and penalty method, it has been proved that any sequence of solutions to a family of approximating optimal control problems converges to an optimal solution of the original problem.
scientific article; zbMATH DE number 7382129
scientific article