  This article studies Gauss-Newton-type methods for over-determined systems to
find solutions to bilevel programming problems. To proceed, we use the
lower-level value function reformulation of bilevel programs and consider
necessary optimality conditions under appropriate assumptions. First under
strict complementarity for upper- and lower-level feasibility constraints, we
prove the convergence of a Gauss-Newton-type method in computing points
satisfying these optimality conditions under additional tractable qualification
conditions. Potential approaches to address the shortcomings of the method are
then proposed, leading to alternatives such as the pseudo or smoothing
Gauss-Newton-type methods for bilevel optimization. Our numerical experiments
conducted on 124 examples from the recently released Bilevel Optimization
LIBrary (BOLIB) compare the performance of our method under different scenarios
and show that it is a tractable approach to solve bilevel optimization problems
with continuous variables.
