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In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method...
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
The finite element approximation of optimal control problems for
semilinear elliptic partial differential equation is considered,
where the control belongs to a finite-dimensional set and state
constraints are given in finitely many points of the domain. Under
the standard linear independency condition on the active gradients
and a strong second-order sufficient optimality condition, optimal
error estimates are derived for locally optimal controls.
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.
The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....
The goal of this paper is to derive some error estimates for the
numerical discretization of some optimal control problems governed
by semilinear elliptic equations with bound constraints on the
control and a finitely number of equality and inequality state
constraints. We prove some error estimates for the optimal
controls in the L∞ norm and we also obtain error estimates
for the Lagrange multipliers associated to the state constraints
as well as for the optimal states and optimal adjoint states.
...
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