New Exact Penalty Function Methods with ?-approximation and Perturbation Convergence for Solving Nonlinear Bilevel Programming Problems

摘要

In this paper, in order to solve a class of nonlinear bilevel programming problems, we equivalently transform the nonlinear bilevel programming problems into corresponding single level nonlinear programming problems by using the Karush-Kuhn-Tucker optimality condition. Then, based on penalty function theory, we construct a smooth approximation method for obtaining optimal solutions of classic l 1-exact penalty function optimality problems, which is equivalent to the single level nonlinear programming problems. Furthermore, using ?-approximate optimal solution theory, we prove convergence of a simple ?-approximate optimal algorithm. Finally, through adding parameters in the constraint set of objective function, we prove some perturbation convergence results for solving the nonlinear bilevel programming problems.