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Mathematical Programs with Multiobjective Generalized Nash Equilibrium Problems in the Constraints

L Guo(guolayne***at***163.com)

Abstract: This paper considers a class of mathematical programs that include multiobjective generalized Nash equilibrium problems in the constraints. For the lower level, we deal with weakly efficient generalized Nash equilibria. Although this kind of problems has some interesting applications, there is no research focusing on it due to the difficulty resulting from its hierarchical structure and the multiplicity of objectives at the lower level. In this paper, we present a single level reformulation for this kind of problems and show the equivalence in terms of global and local minimizers. We find that the reformulation is a special case of a mathematical program with equilibrium constraints which is extensively studied in the literature.

Keywords: Multiobjective optimization; bilevel program; generalized Nash equilibrium

Category 1: Applications -- OR and Management Sciences

Citation:

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Entry Submitted: 12/11/2019
Entry Accepted: 12/12/2019
Entry Last Modified: 12/11/2019

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