Stopping rules and backward error analysis 
                for bound-constrained optimization

        Serge~Gratton,  Melodie Mouffe and Philippe L. Toint

               Report 09/13              8 October 2009

Termination criteria for the iterative solution of bound-constrained
optimization problems are examined in the light of backward error analysis.
It is shown that the problem of determining a suitable perturbation on the
problem's data corresponding to the definition of the backward error is
analytically solvable under mild assumptions.  Moreover, a link between
existing termination criteria and this solution is clarified, indicating that
some standard measures of criticality may be interpreted in the sense of
backward error analysis. The backward error problem is finally considered from
the multicriteria optimization point of view and some numerical illustration
is provided.