Duality of regularizations and hullfunctions for mathematical programming problems (Q1342426)

In practice there exist nonlinear programming problems which are ill- posed (the feasible set of the problem is empty or the objective tends to infinity over the nonempty feasible set). In such situations we need information for a correction of the original problem in ``some minimal manner''. By introducing parameters and additional functions we improve the properties of the given problem. Notations from the literature for this concept are regularization, stabilization, hullfunction etc. The content of this paper is the investigation of duality aspects of such regularizations and the formation of hullfunctions on the other hand. Among others it is shown that a regularization of the primal problem corresponds to a hullfunction of the dual problem, and vice versa. Further that the forming of hullfunctions in the primal problem corresponds to some regularizations of the dual problem. Results of this paper can inspire some applications to solution methods for parametric and multicriteria optimization.