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Necessary conditions in multiobjective optimization with equilibrium constraints. (English) Zbl 1146.90508

Summary: 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.

MSC:

90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
49J40 Variational inequalities
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References:

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