Starting from a study for a class of prox-penalization and splitting methods to solve some variational inequalities based on general maximal monotone operators in Hilbert spaces, the authors obtain solutions for several optimal control problems with the state variables and controls coupled by elliptic equations. The paper concludes with robustness and stability for numerical approximation errors and pertinent references.
Reviewer’s remark: This is a significant work also in connection with adequate numerical methods.