id: 05859898
dt: j
an: 05859898
au: Herzog, Roland; Sachs, Ekkehard
ti: Preconditioned conjugate gradient method for optimal control problems with
    control and state constraints.
so: SIAM J. Matrix Anal. Appl. 31, No. 5, 2291-2317 (2010).
py: 2010
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: preconditioned conjugate gradient method; saddle point problems; optimal
    control of partial differential equations; control and state
    constraints; multigrid method
ci: 
li: doi:10.1137/090779127
ab: Summary: Optimality systems and their linearizations arising in optimal
    control of partial differential equations with pointwise control and
    (regularized) state constraints are considered. The Preconditioned
    Conjugate Gradient (PCG) method in a nonstandard inner product is
    employed for their efficient solution. Preconditioned condition numbers
    are estimated for problems with pointwise control constraints, mixed
    control-state constraints, and of Moreau-Yosida penalty type. Numerical
    results for elliptic problems demonstrate the performance of the PCG
    iteration. Regularized state-constrained problems in three dimensions
    with more than 750,000 variables are solved.
rv: