Lipschitzian properties of the infinite-diemsional dual pair

Abstract

We apply the concept of coderivative and other tools from variational analysis to study the stability of the feasible sets of both, the primal and the dual problem in infinite-dimensional linear optimization with infinitely many explicit constraints and an additional conic constraint.

After providing some specific duality results for our dual pair, we study the Lipschitz-like property of both mappings and also give bounds for the associated Lipschitz moduli.

The situation for the dual turns out to be much more involved than the case of the primal problem.

Details