Levenberg–Marquardt method and partial exact penalty parameter selection in bilevel optimization

Abstract We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into single-level problem by means lower-level optimal value function reformulation. Subsequently, based on partial calmness concept, build an equation system, which is parameterized corresponding exact penalization parameter. then design and analyze Levenberg–Marquardt method solve this parametric system equations. Considering fact selection parameter critical issue when numerically solving reformulation, conduct careful experimental study effect, context method, while using Bilevel Optimization LIBrary (BOLIB) series test problems. This enables construction some safeguarding mechanisms for practical robust convergence can also serve as base penalty other algorithms. compare introduced paper existing algorithms similar nature.