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Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints

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Abstract

We study multiobjective optimization problems with equilibrium constraints (MOPECs) described by parametric generalized equations in the form

$$0\in G(x,y)+Q(x,y),$$

where both mappings G and Q are set-valued. Such models arise particularly from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications by using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex while nondifferentiable data.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, USA

    T. Q. Bao & B. S. Mordukhovich

  2. Department of Operational Research, University of Delhi, Delhi, India

    P. Gupta

Authors
  1. T. Q. Bao
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  2. P. Gupta
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  3. B. S. Mordukhovich
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Correspondence to B. S. Mordukhovich.

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Communicated by F. Giannessi.

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Bao, T.Q., Gupta, P. & Mordukhovich, B.S. Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints. J Optim Theory Appl 135, 179–203 (2007). https://doi.org/10.1007/s10957-007-9209-x

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  • DOI: https://doi.org/10.1007/s10957-007-9209-x

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