On coderivatives and Lipschitzian properties of the dual pair in optimization

Abstract

In this paper we apply the concept of coderivative and other tools from the generalized differentiation theory for set-valued mappings 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 shows much more involved than the case of the primal problem.