Prof. Dr. Abderrahim Jourani (Uni. Dijon)
<p>
  <b>Error bound characterizations of the conical constraint
qualification in convex programming
  </b>
<p>
This talk deals with error bound characterizations of the conical constraint
qualification
(CCQ) for convex inequality systems in a Banach space <i>X</i>.
We establish necessary
and sufficient conditions for a closed convex set <i>S</i>
defined by a convex function <i>g</i> to have CCQ. Our results show that these characterizations hold in very
special situations. We
construct technical examples showing that these characterizations are limited to
these situations. We introduce a new condition in terms of the gauge function
which allows us
to give an error bound characterization of convex nondifferentiable systems and
to obtain as a direct consequence different characterizations of the concept of
the strong conical hull intersection property (CHIP) for a finite collection of
convex sets.