Exact Penalty Method for the Nonlinear Bilevel Programming Problem

作     者：PAN Qingfei AN Zhonghua QI Hui 

作者机构：Department of Physics and Mechanics-Electronic EngineeringSanming University Sanming 365004 Fujian China Department of Mathematics and Measure Economics Hu-bei University of Education Wuhan 430205 Hubei China Department of Mathematics and Computer SanmingUniversity Sanming 365004 Fujian China 

出 版 物：《Wuhan University Journal of Natural Sciences》 (武汉大学学报（自然科学英文版）)

年 卷 期：2010年第15卷第6期

页      面：471-475页

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Supported by the Key Project on Science and Technology of Hubei Provincial Department of Education (D20103001) 

主　　题：convex-quadratic programming nonlinear bilevel programming Kuhn-Tucker optimality condition penalty function method optimal solution 

摘      要：In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint ***,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a *** prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution ***,we propose an algorithm for the nonlinear bilevel programming *** numerical results show that the algorithm is feasible and efficient.