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Computers & Mathematics with Applications
Volume 49, Issues 7-8, May-June 2005, Pages 1243-1253
 
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doi:10.1016/j.camwa.2004.05.014    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2005 Published by Elsevier Ltd.

Bilevel decision via variational inequalities*

Yeong-Cheng LiouE-mail The Corresponding Author and Jen-Chih YaoCorresponding Author Contact Information, E-mail The Corresponding Author

Department of Information Management, Cheng Shiu University Kaohsiung Country 833, Taiwan, R.O.C. Department of Applied Mathematics, National Sun Yat-sen University Kaohsiung, Taiwan 80424, R.O.C.

Accepted 1 May 2004. 
Available online 4 August 2005.

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Abstract

In this paper, we introduce the group decision problems in a bilevel programming structure, and its corresponding optimization with equilibrium constraints (MPEC for short) problems. For these models, we establish new existence results, which extend some known results to infinite-dimensional space setting. We also establish the links between group decision problems in a bilevel programming structure and its corresponding MPEC problems in Banach spaces. An interesting example about the mean-variance portfolio optimization is given and the existence and uniqueness results for its corresponding MPEC problems are obtained.

Keywords: Bilevel programming; Variational inequality problems; Stackelberg problems; MPEC problems; Group decision-making problems; Reflexive Banach spaces; Mean-variance portfolio optimization


 
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