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Global minima for semilinear optimal control problems

by Ahmad Ali, Klaus Deckelnick, Michael Hinze.

Series: 2015-08, Preprints

49J20 Optimal control problems involving partial differential equations
65M12 Stability and convergence of numerical methods

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 the discretization parameter the sequence of discrete solutions converges to a global solution of the corresponding limit problem. Numerical examples with unique global solutions are presented.

optimal control, semilinear PDE, uniqueness of global solution