Numerical algorithms for one and two target optimal controls

In this paper one and two target optimal controls of a linear diffusion equation are considered. These problems can be formulated as nonlinear, PDE-constrained optimization problems in infinite dimension. We consider two formulations, one having an inequality constraint mandating the primary target to be satisfied within a given tolerance 2, and the other having weighted norms in the cost function to fulfill the same requirement. In this paper we develop iterative numerical algorithms that estimate the weights, α, in terms of 2. This result allows us to estimate the solution of the inequality constrained optimization, which is generally difficult and computationally expensive, by the solution of the optimization problem having the weighted norms.