A Filter Method to Solve Nonlinear Bilevel Programming Problems

摘要

Filter methods, introduced by Fletcher and Leyffer for nonlinear programming are characterized by the use of the dominance concept of multiob-jective optimization, instead of a penalty parameter whose adjustment can be problematic. This paper presents a way to implement a filter based approach to solve a nonlinear bilevel programming problem in a linear approximations framework. The approach presented is based on the trust region idea from nonlinear programming, combined with filter-SQP algorithm, smooth and active sets techniques. The restoration procedure introduced in our algorithm consists in computing a rational solution.