On Lipschitzian stability of optimal solutions of parametrized semi-infinite programs

The paper studies continuity properties of optimal solutions of parametrized semi-infinite programming problems. The involved constraints are formulated in a form of cone constraints and then a slightly modified general result of Shapiro and Bonnans on Lipschitzian stability of optimal solutions is applied. It is shown that under certain second-order sufficient conditions, optimal solutions of the semi-infinite programs are Lipschitzian stable provided a regularity assumption related to a linearization of the considered programs is satisfied.