A Bundle Algorithm Applied to Bilevel Programming Problems with Non-Unique Lower Level Solutions

In the paper, the question is investigated if a bundle algorithm can be used to compute approximate solutions for bilevel programming problems where the lower level optimal solution is in general not uniquely determined. To give a positive answer to this question, an appropriate regularization approach is used in the lower level. In the general case, the resulting algorithm computes an approximate solution. If the problem proves to have strongly stable lower level solutions for all parameter values in a certain neighborhood of the stationary solutions of the bilevel problem, convergence to stationary solutions can be shown.