An optimal control problem governed by a bilinear elliptic equation is considered. Thisproblem is solved by the sequential quadratic programming (SQP) method in aninfinite-dimensional framework. In each level of this iterative method the solution oflinear-quadratic subproblem is computed by a Galerkin projection using proper orthogonaldecomposition (POD). Thus, an approximate (inexact) solution of the subproblem isdetermined. Based on a POD a-posteriori error estimator developed byTröltzsch and Volkwein [Comput. Opt. Appl. 44 (2009) 83–115]the difference of the suboptimal to the (unknown) optimal solution of the linear-quadraticsubproblem is estimated. Hence, the inexactness of the discrete solution is controlled insuch a way that locally superlinear or even quadratic rate of convergence of the SQP isensured. Numerical examples illustrate the efficiency for the proposed approach.
