A New Descent Method for Solving Ill-Posed Bilevel Programming Problems via Maxmin Model

The results of optimistic model and pessimistic model are always not efficient for practical application because they are two extreme possibilities for ill-posed bilevel programming problem. This paper presents a new model by transferring Minmax model to a Maxmin model to solve above shortcoming. And we prove, by this transformation, a more practical value between the optimistic value and the pessimistic value can be achieved. Then, a new descent algorithm is developed to solve this new model by considering the satisfying degree of the lower level. Finally, an illustrated numerical example is demonstrated to show the proposed new model and algorithm are feasible and we can get a better result from all the iterated points by this Maxmin model than by the two extreme models.