Acta mathematica scientia, Series B >
A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM
Received date: 2008-10-28
Revised date: 2010-07-26
Online published: 2011-03-20
Supported by
This research was partially supported by the National Science Foundation of China (70771080) and Social Science Foundation of Ministry of Education (10YJC630233).
The penalty function method, presented many years ago, is an important numerical method for the mathematical programming
problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function
approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our
algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
WAN Zhong-Ping , WANG Guang-Min , LV Yi-Bing . A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 652 -660 . DOI: 10.1016/S0252-9602(11)60265-8
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