A penalty method with trust-region mechanism for nonlinear bilevel optimization problem

We present a penalty method with trust-region technique for nonlinear bilevel optimization problem in this paper. This method follows Dennis, El-Alem, and Williamson active set idea and penalty method to transform the nonlinear bilevel optimization problem to unconstrained optimization problem. This method maybe simpler than similar ideas and it does not need to compute a base of the null space. A trust-region technique is used to globalize the algorithm. Global convergence theorem is presented and applications to mathematical programs with equilibrium constraints are given.