A neural network for solving nonlinear multilevel programming problems

Authors:
Feng Xiangdong;Hu Guanghua
Affiliations:
School of Mathematics and Statistics of Yunnan University, Yunnan Kunming, P.R. China and The Engineering & Technical College of Chengdu University of Technology, Sichuan, Leshan, P.R. China;School of Mathematics and Statistics of Yunnan University, Yunnan Kunming, P.R. China
Venue:
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Year:
2009

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Abstract

This paper aims at utilizing the dynamic behavior of artificial neural networks to solve nonlinear multilevel programming (MLP) problems. Across complementarily slackness conditions base on entropic regularization, the optimization problem is converted into a system of nonlinear differential equations through use of an energy function and Lagrange multipliers. To solve the resulting differential equations, a steepest descent search technique is used. This proposed nontraditional algorithm is efficient for solving complex problems, and MLP problems can be solved on a real time basis. To illustrate the approach, several numerical examples are solved and compared.