A two-phase strategy for control constrained elliptic optimal control problems

A Multigrid Scheme for Elliptic Constrained Optimal Control Problems

A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational ...

A New Optimal Solution Concept for Fuzzy Optimal Control Problems

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

Primal-Dual Strategy for State-Constrained Optimal Control Problems

State constrained optimal control problems represent severe analytical and numerical challenges. A numerical algorithm based on an active set strategy involving primal as well as dual variables, suggested by a generalized Moreau-Yosida regularization of the state constraint is proposed and analyzed. Numerical examples are included.

Preconditioned Solution of State Gradient Constrained Elliptic Optimal Control Problems

Elliptic optimal control problems with pointwise state gradient constraints are considered. A quadratic penalty approach is employed together with a semismooth Newton iteration. Three different preconditioners are proposed and the ensuing spectral properties of the preconditioned linear Newton saddle-point systems are analyzed in dependence on the penalty parameter. A new bound for the smallest...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)