Preprint A303/2004
Primal error bounds based on the augmented Lagrangian and Lagrangian relaxation algorithms

Solodov Mikhail | Alexey, Izmailov

**Keywords: **
Error bound | augmented Lagrangian | Lagrangian relaxation | sensitivity

For a given iterate generated by
the augmented Lagrangian or the Lagrangian relaxation based
method, we derive computable estimates for the distance to
the primal solution
of the underlying optimization problem.
The estimates are obtained
using some recent contributions to the sensitivity theory,
under appropriate first or second order
sufficient optimality conditions. The given estimates
hold in situations where
known (algorithm-independent) error bounds may not apply.
Examples are provided which show that the estimates are sharp.