OPTIMAL CONTROL PROBLEMS FOR SEMILINEAR EVOLUTION EQUATIONS

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 Nonsmooth, Semilinear Parabolic Equations

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...

Anti-periodic Problems for Semilinear Partial Neutral Evolution Equations†

We study the anti-periodic problem for the semilinear partial neutral evolution equation in the form d dt [u(t) + h(t, u(t))] + Au(t) = f(t, u(t)), t ∈ R in a Banach space X, where h, f are given X-valued functions, and −A : D(A) ⊆ X → X is the infinitesimal generator of a compact analytic semigroup. Some new theorems concerning the existence of anti-periodic mild solutions for the problem are ...

Optimal Control of Semilinear Elliptic Obstacle Problems