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Journal of Industrial and Management Optimization (JIMO)
 

Multistage hierarchical optimization problems with multi-criterion objectives

Pages: 103 - 115, Volume 7, Issue 1, February 2011      doi:10.3934/jimo.2011.7.103

 
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Roxin Zhang - Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, United States (email)
Bao Truong - Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, United States (email)
Qinghong Zhang - Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, United States (email)

Abstract: A hierarchical optimization (or bilevel programming) problem consists of a decision maker called the leader who is interested in optimizing an objective function that involves with the decisions from another decision maker called the follower whose decisions are based in part on the policies made by the leader. However, if the planning horizon expands into an extended period of time, it may be unrealistic for either players to commit to the original decisions so there is a desire to break the problem into stages and the leader may wish to reevaluate the follower's response at each stage. In this article, we propose a multistage hierarchical optimization problem with the leader's objective consisting of multiple criteria and study the optimality conditions of such problems using an extremal principle of Mordukhovich.

Keywords:  Hierarchical optimization, multistage bilevel programming, multiobjective optimization, normal coderivative.
Mathematics Subject Classification:  Primary: 49J52, 90C46; Secondary: 49J53.

Received: October 2009;      Revised: October 2010;      Available Online: January 2011.

 References