The classical Eckart-Young theorems says that that, given a
nonsingular matrix A the infimum of the norm of a matrix B for which
A+B is singular is equal to the reciprocal of the norm of the inverse of
A. In view of this result, the standard condition number of a matrix
is just the normalized reciprocal to the distance to nonsingularity. In
recent years attempts have been
made to extend this theorem to mappings describing feasibility
conditions,
e.g. systems of inequalities, as well as optimality conditions,
complementarity problems and variational inequalities, all of which
can be posed as solving ``generalized equations'' for set-valued mappings.
In the talk, various properties and
characterizations already known in classical context are extended
to obtain result modeled on the Eckart-Young theorem.
[Based on joint works with A.S.Lewis and R.T.Rockafellar]
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