Global minima for semilinear optimal control problems

Global minima for semilinear optimal control problems

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global minimum. This condition can be explicitly evaluated at the discrete level. Furthermore, we prove that if the above condition holds uniformly with respect to t...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Optimal Control of Semilinear Elliptic Obstacle Problems

Discretization Methods for Semilinear Parabolic Optimal Control Problems

We consider an optimal control problem described by semilinear parabolic partial differential equations, with control and state constraints. Since this problem may have no classical solutions, it is also formulated in the relaxed form. The classical control problem is then discretized by using a finite element method in space and the implicit Crank-Nicolson midpoint scheme in time, while the co...

Verifying global minima for L2 minimization problems

We consider the least-squares (L2) triangulation problem and structure-and-motion with known rotatation, or known plane. Although optimal algorithms have been given for these algorithms under an L-infinity cost function, finding optimal least-squares (L2) solutions to these problems is difficult, since the cost functions are not convex, and in the worst case can have multiple minima. Iterative ...