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.

Anexos:

• izmsol04al-lr.pdf