Prox-penalization and splitting methods for constrained variational problems. (English) Zbl 1229.90225
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.
Reviewer’s remark: This is a significant work also in connection with adequate numerical methods.
Reviewer: Vasile Postolică (Piatra Neamt)
MSC:
90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
49J20 | Existence theories for optimal control problems involving partial differential equations |
65K10 | Numerical optimization and variational techniques |