Journal of Optimization Theory and Applications

, Volume 135, Issue 2, pp 179–203 | Cite as

Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints



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.


Variational analysis Nonsmooth and multiobjective optimization Variational inequalities Equilibrium constraints Bilevel programming Necessary optimality conditions Generalized differentiation 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA
  2. 2.Department of Operational ResearchUniversity of DelhiDelhiIndia

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