In 1997, Macal and Hurter have found that adding a constraint to the lower level problem, which is not active at the computed global optimal solution, can destroy global optimality. In this paper this property is reconsidered and it is shown that this solution remains locally optimal under inner semicontinuity of the original solution set mapping. In the second part of the paper we prove that adding a variable in the linear lower level problem can also destroy global optimality. But here the solution remains locally optimal, provided the optimal solution in the lower level was dual non-degenerated.
Preprint 2011-01, Department of Mathematics and Computer Science, TU Bergakademie Freiberg, Germany, 2011