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Necessary optimality conditions for multiobjective bilevel programs

Jane Ye (janeye***at***uvic.ca)

Abstract: The multiobjective bilevel program is a sequence of two optimization problems where the upper level problem is multiobjective and the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of all lower level problems near the optimal solution, we present various optimality conditions by replacing the lower level problem by its KKT conditions. For the general multiobjective bilevel problem we derive necessary optimality conditions by considering a combined problem where both the value function and the KKT condition of the lower level problem are involved in the constraints.

Keywords: multiobjective optimization, preference, necessary optimality

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Other Topics (Multi-Criteria Optimization )

Category 3: Other Topics (Game Theory )


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Entry Submitted: 03/03/2010
Entry Accepted: 03/03/2010
Entry Last Modified: 08/28/2010

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