This paper describes necessary and suucient optimality conditions for bilevel programming problems with quadratic strictly convex lower levels. By examining the local geometry of these problems we establish that the set of feasible directions at a given point is composed of a nite union of convex cones. Based on this result, we show that the optimality conditions are simple generalizations of t...

In 1997, Macal and Hurter [7] 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 th...