A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

doi:10.1016/S0252-9602(11)60265-8

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (2): 652-660.doi: 10.1016/S0252-9602(11)60265-8

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A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

WAN Zhong-Ping, WANG Guang-Min, LV Yi-Bing

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China； School of Economics and Management, China University of Geosciences, Wuhan 430074, China； Institute of Information and Mathematics, Yangtze University, Jingzhou, Hubei, China

Received:2008-10-28 Revised:2010-07-26 Online:2011-03-20 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).

Abstract

Abstract:

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.

Key words: Nonlinear bilevel programming, penalty function approach, dual-relax strategy

CLC Number:

90C26

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.

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A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

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